diff --git a/data/.dir-locals.el b/data/.dir-locals.el new file mode 100644 index 0000000000000000000000000000000000000000..54101ba0515d35351d3e8dd83a7ba402f8c9d849 --- /dev/null +++ b/data/.dir-locals.el @@ -0,0 +1,22 @@ +((python-mode + (eval . (setq flycheck-python-flake8-executable + (expand-file-name ".venv/bin/python" (locate-dominating-file + default-directory + ".dir-locals.el")))) + (eval . (setq flycheck-python-pylint-executable + (expand-file-name ".venv/bin/python" (locate-dominating-file + default-directory + ".dir-locals.el")))) + (eval . (setq flycheck-python-mypy-executable + (expand-file-name ".venv/bin/mypy" (locate-dominating-file + default-directory + ".dir-locals.el")))) + (eval . (setq flycheck-python-pycompile-executable + (expand-file-name ".venv/bin/python" (locate-dominating-file + default-directory + ".dir-locals.el"))))) + (rst-mode + (eval . (setq flycheck-rst-sphinx-executable + (expand-file-name ".venv/bin/sphinx-build" (locate-dominating-file + default-directory + ".dir-locals.el")))))) diff --git a/data/.readthedocs.yml b/data/.readthedocs.yml new file mode 100644 index 0000000000000000000000000000000000000000..a386f6b426c9f61b1d557708b9e194ac3c2c188c --- /dev/null +++ b/data/.readthedocs.yml @@ -0,0 +1,19 @@ +version: 2 + +# Set the version of Python and other tools you might need +build: + os: ubuntu-lts-latest + tools: + python: latest + +# Build documentation in the docs/ directory with Sphinx +sphinx: + configuration: docs/source/conf.py + +# If using Sphinx, optionally build your docs in additional formats such as PDF +formats: all + +# Optionally declare the Python requirements required to build your docs +python: + install: + - requirements: docs/requirements.txt diff --git a/data/.zenodo.json b/data/.zenodo.json new file mode 100644 index 0000000000000000000000000000000000000000..33af82a8d13c0eb10bcaed93ba1d69acac92019c --- /dev/null +++ b/data/.zenodo.json @@ -0,0 +1,92 @@ +{ + "creators": [ + { + "orcid": "0000-0003-4513-5139", + "affiliation": "Freie Universität Berlin", + "name": "Naumann, Jan" + }, + { + "orcid": "0000-0001-5534-6103", + "affiliation": "Freie Universität Berlin", + "name": "Schmoll, Philipp" + }, + { + "orcid": "0009-0003-7734-1209", + "affiliation": "Freie Universität Berlin", + "name": "Losada, Roberto" + }, + { + "orcid": "0000-0002-6224-1964", + "affiliation": "Freie Universität Berlin", + "name": "Wilde, Frederik" + }, + { + "affiliation": "Freie Universität Berlin", + "name": "Krein, Finn" + } + ], + + "contributors": [ + { + "orcid": "0009-0006-8139-8648", + "affiliation": "University of Cologne", + "name": "Weerda, Erik Lennart", + "type": "Researcher" + }, + { + "orcid": "0000-0002-8283-1005", + "affiliation": "University of Cologne", + "name": "Rizzi, Matteo", + "type": "Supervisor" + }, + { + "orcid": "0000-0003-3033-1292", + "affiliation": "Freie Universität Berlin", + "name": "Eisert, Jens", + "type": "Supervisor" + } + ], + + "description": "A versatile tensor network library for variational ground state simulations in two spatial dimensions.", + + "license": "GPL-3.0-or-later", + + "title": "variPEPS (Python version)", + + "related_identifiers": [ + { + "identifier": "https://doi.org/10.21468/SciPostPhysLectNotes.86", + "relation": "isDocumentedBy", + "resource_type": "publication-article" + }, + { + "identifier": "https://doi.org/10.1103/PhysRevB.111.235116", + "relation": "isDocumentedBy", + "resource_type": "publication-article" + }, + { + "identifier": "https://doi.org/10.1103/g5gm-tzf8", + "relation": "isDocumentedBy", + "resource_type": "publication-article" + }, + { + "identifier": "https://varipeps.readthedocs.io/en/stable/", + "relation": "isDocumentedBy", + "resource_type": "publication-softwaredocumentation" + } + ], + + "keywords": [ + "physics", + "automatic-differentiation", + "peps", + "tensor-networks", + "variational-optimization", + "quantum-many-body", + "quantum-many-body-physics" + ], + + "communities": [ + {"identifier": "crc183"} + ] +} diff --git a/data/CITATION.cff b/data/CITATION.cff new file mode 100644 index 0000000000000000000000000000000000000000..4e51f718845bf621445f2639c725d5c5ca00bc51 --- /dev/null +++ b/data/CITATION.cff @@ -0,0 +1,58 @@ +# This CITATION.cff file was generated with cffinit. +# Visit https://bit.ly/cffinit to generate yours today! + +cff-version: 1.2.0 +title: variPEPS (Python version) +message: >- + If you use this software, please cite it using the + metadata from this file. +type: software +authors: + - given-names: Jan + family-names: Naumann + email: j.naumann@fu-berlin.de + affiliation: Freie Universität Berlin + orcid: 'https://orcid.org/0000-0003-4513-5139' + - given-names: Schmoll + family-names: Philipp + affiliation: Freie Universität Berlin + orcid: 'https://orcid.org/0000-0001-5534-6103' + email: philipp.schmoll@fu-berlin.de + - given-names: Losada + family-names: Roberto + affiliation: Freie Universität Berlin + orcid: 'https://orcid.org/0009-0003-7734-1209' + email: roberto.losada@fu-berlin.de + - given-names: Wilde + orcid: 'https://orcid.org/0000-0002-6224-1964' + family-names: Frederik + affiliation: Freie Universität Berlin + - given-names: Krein + family-names: Finn +identifiers: + - type: doi + value: 10.21468/SciPostPhysLectNotes.86 + description: Journal article with the description of the method + - type: doi + value: 10.1103/PhysRevB.111.235116 + description: Journal article with description of the split-CTMRG method + - type: doi + value: 10.1103/g5gm-tzf8 + description: Journal article with description of the triangular CTMRG method + - type: doi + value: 10.5281/zenodo.10852390 + description: Zenodo DOI for current version of the code +repository-code: 'https://github.com/variPEPS/variPEPS_Python' +url: 'https://varipeps.readthedocs.io/en/stable' +abstract: >- + A versatile tensor network library for variational ground + state simulations in two spatial dimensions +keywords: + - physics + - automatic-differentiation + - peps + - tensor-networks + - variational-optimization + - quantum-many-body + - quantum-many-body-physics +license: GPL-3.0-or-later diff --git a/data/CMakeLists.txt b/data/CMakeLists.txt new file mode 100644 index 0000000000000000000000000000000000000000..67a983d24e7c796d6d777d7691fe30ee8595ca44 --- /dev/null +++ b/data/CMakeLists.txt @@ -0,0 +1,60 @@ +# Set the minimum CMake version and policies for highest tested version +cmake_minimum_required(VERSION 3.15...3.27) + +# Set default build type in CMake if skbuild is set +message(STATUS "CMAKE_BUILD_TYPE set to '${CMAKE_BUILD_TYPE}'") + +# Set up the project and ensure there is a working C++ compiler +project(varipeps_extensions LANGUAGES CXX) + +# Try to import all Python components potentially needed by nanobind +find_package(Python 3.11 + REQUIRED COMPONENTS Interpreter Development.Module + OPTIONAL_COMPONENTS Development.SABIModule) + +# Import nanobind through CMake's find_package mechanism +execute_process( + COMMAND /usr/bin/env python3 -m nanobind --cmake_dir + OUTPUT_STRIP_TRAILING_WHITESPACE OUTPUT_VARIABLE nanobind_ROOT) +find_package(nanobind CONFIG REQUIRED) + +# Find jaxlib include dir +IF (WIN32) + execute_process( + COMMAND python -c "import inspect; import jaxlib; import pathlib; p = pathlib.Path(inspect.getfile(jaxlib)); print(p.parent / 'include')" + OUTPUT_STRIP_TRAILING_WHITESPACE OUTPUT_VARIABLE jaxlib_INCLUDE_DIR) +ELSE() + execute_process( + COMMAND /usr/bin/env python3 -c "import inspect; import jaxlib; import pathlib; p = pathlib.Path(inspect.getfile(jaxlib)); print(p.parent / 'include')" + OUTPUT_STRIP_TRAILING_WHITESPACE OUTPUT_VARIABLE jaxlib_INCLUDE_DIR) +ENDIF() + + +# We are now ready to compile the actual extension module +nanobind_add_module( + # Name of the extension + _svd_only_u_vt + + # Target the stable ABI for Python 3.12+, which reduces + # the number of binary wheels that must be built. This + # does nothing on older Python versions + STABLE_ABI + + # Build libnanobind statically and merge it into the + # extension (which itself remains a shared library) + # + # If your project builds multiple extensions, you can + # replace this flag by NB_SHARED to conserve space by + # reusing a shared libnanobind across libraries + NB_STATIC + + # Source code goes here + varipeps/utils/extensions/svd_ffi.cpp +) + +target_include_directories(_svd_only_u_vt PRIVATE "${jaxlib_INCLUDE_DIR}") + +# target_link_libraries(_svd_only_vt PRIVATE lapack) + +# Install directive for scikit-build-core +install(TARGETS _svd_only_u_vt LIBRARY DESTINATION varipeps/utils/extensions) diff --git a/data/LICENSE b/data/LICENSE new file mode 100644 index 0000000000000000000000000000000000000000..dfc3a6e6c9d9c663d64d7f78980ef2785b909718 --- /dev/null +++ b/data/LICENSE @@ -0,0 +1,674 @@ + GNU GENERAL PUBLIC LICENSE + Version 3, 29 June 2007 + + Copyright (C) 2007 Free Software Foundation, Inc. + Everyone is permitted to copy and distribute verbatim copies + of this license document, but changing it is not allowed. + + Preamble + + The GNU General Public License is a free, copyleft license for +software and other kinds of works. + + The licenses for most software and other practical works are designed +to take away your freedom to share and change the works. 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It is safest +to attach them to the start of each source file to most effectively +state the exclusion of warranty; and each file should have at least +the "copyright" line and a pointer to where the full notice is found. + + varipeps + Copyright (C) 2021-2024 Jan Naumann and variPEPS contributors + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU General Public License for more details. + + You should have received a copy of the GNU General Public License + along with this program. If not, see . + +Also add information on how to contact you by electronic and paper mail. + + If the program does terminal interaction, make it output a short +notice like this when it starts in an interactive mode: + + Copyright (C) 2021 qmio / peps + This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. + This is free software, and you are welcome to redistribute it + under certain conditions; type `show c' for details. + +The hypothetical commands `show w' and `show c' should show the appropriate +parts of the General Public License. Of course, your program's commands +might be different; for a GUI interface, you would use an "about box". + + You should also get your employer (if you work as a programmer) or school, +if any, to sign a "copyright disclaimer" for the program, if necessary. +For more information on this, and how to apply and follow the GNU GPL, see +. + + The GNU General Public License does not permit incorporating your program +into proprietary programs. If your program is a subroutine library, you +may consider it more useful to permit linking proprietary applications with +the library. If this is what you want to do, use the GNU Lesser General +Public License instead of this License. But first, please read +. diff --git a/data/README.md b/data/README.md new file mode 100644 index 0000000000000000000000000000000000000000..952ca97d2540eefe98d6077a2a315a59a41111b5 --- /dev/null +++ b/data/README.md @@ -0,0 +1,96 @@ +![Logo of the variPEPS library with a triangular-PEPS norm as picture and "variPEPS -- Variational PEPS Library" as text right of it](https://github.com/variPEPS/variPEPS_Python/raw/main/docs/source/images/logo.svg) + +# variPEPS -- Versatile tensor network library for variational ground state simulations in two spatial dimensions. + +[![DOI](https://zenodo.org/badge/773767511.svg)](https://zenodo.org/doi/10.5281/zenodo.10852390) +[![Documentation Status](https://readthedocs.org/projects/varipeps/badge/?version=latest)](https://varipeps.readthedocs.io/en/stable/?badge=latest) +[![PyPI - Version](https://img.shields.io/pypi/v/varipeps)](https://pypi.org/project/variPEPS/) + +variPEPS is the Python variant of the tensor network library developed for +variational ground state simulations in two spatial dimensions applying gradient +optimization using automatic differentation. + +For a detailed report on the method, please see our publications listed at the +end of this readme. + +## Installation +### Installation using pip +The current version of the variPEPS Python package is available on +[PyPI](https://pypi.org/project/variPEPS/). +It can be easily installed by using the Python package manager pip: +```bash +$ python3 -m pip install variPEPS +``` + +## Usage + +For detailed information how to use the package we want to point out to the +[documentation of the project](https://varipeps.readthedocs.io/en/stable). + +## Citation + +We are happy if you want to use the framework for your research. For the +citation of our work we ask to use the following references (the publications +with the method description and the Zenodo reference for this Git repository): +* J. Naumann, E. L. Weerda, M. Rizzi, J. Eisert, and P. Schmoll, An introduction + to infinite projected entangled-pair state methods for variational ground + state simulations using automatic differentiation, SciPost Phys. Lect. Notes + 86 (2024), + doi:[10.21468/SciPostPhysLectNotes.86](https://doi.org/10.21468/SciPostPhysLectNotes.86). +* J. Naumann, E. L. Weerda, J. Eisert, M. Rizzi and P. Schmoll, Variationally + optimizing infinite projected entangled-pair states at large bond dimensions: + A split corner transfer matrix renormalization group approach, Phys. Rev. B + 111, 235116 (2025), + doi:[10.1103/PhysRevB.111.235116](https://doi.org/10.1103/PhysRevB.111.235116). +* J. Naumann, J. Eisert, P. Schmoll, Variational optimization of projected + entangled-pair states on the triangular lattice, + [arXiv:2510.04907](https://arxiv.org/abs/2510.04907) +* J. Naumann, P. Schmoll, R. Losada, F. Wilde, and F. Krein, [variPEPS (Python + version)](https://zenodo.org/doi/10.5281/zenodo.10852390), Zenodo. + +The BibTeX code for these references are: +```bibtex +@article{10.21468/SciPostPhysLectNotes.86, + title={{An introduction to infinite projected entangled-pair state methods for variational ground state simulations using automatic differentiation}}, + author={Jan Naumann and Erik Lennart Weerda and Matteo Rizzi and Jens Eisert and Philipp Schmoll}, + journal={SciPost Phys. Lect. Notes}, + pages={86}, + year={2024}, + publisher={SciPost}, + doi={10.21468/SciPostPhysLectNotes.86}, + url={https://scipost.org/10.21468/SciPostPhysLectNotes.86}, +} + +@article{PhysRevB.111.235116, + title = {Variationally optimizing infinite projected entangled-pair states at large bond dimensions: A split corner transfer matrix renormalization group approach}, + author = {Naumann, Jan and Weerda, Erik L. and Eisert, Jens and Rizzi, Matteo and Schmoll, Philipp}, + journal = {Phys. Rev. B}, + volume = {111}, + issue = {23}, + pages = {235116}, + numpages = {12}, + year = {2025}, + month = {Jun}, + publisher = {American Physical Society}, + doi = {10.1103/PhysRevB.111.235116}, + url = {https://link.aps.org/doi/10.1103/PhysRevB.111.235116} +} + +@misc{naumann2025variationaloptimizationprojectedentangledpair, + title={Variational optimization of projected entangled-pair states on the triangular lattice}, + author={Jan Naumann and Jens Eisert and Philipp Schmoll}, + year={2025}, + eprint={2510.04907}, + archivePrefix={arXiv}, + primaryClass={cond-mat.str-el}, + url={https://arxiv.org/abs/2510.04907}, +} + +@software{naumann_varipeps_python, + author = {Jan Naumann and Philipp Schmoll and Roberto Losada and Frederik Wilde and Finn Krein}, + title = {{variPEPS (Python version)}}, + howpublished = {Zenodo}, + url = {https://doi.org/10.5281/ZENODO.10852390}, + doi = {10.5281/ZENODO.10852390}, +} +``` diff --git a/data/docs/LICENSE b/data/docs/LICENSE new file mode 100644 index 0000000000000000000000000000000000000000..7d4f96c54aa155a17387e64501c50b6a0469932c --- /dev/null +++ b/data/docs/LICENSE @@ -0,0 +1,427 @@ +Attribution-ShareAlike 4.0 International + +======================================================================= + +Creative Commons Corporation ("Creative Commons") is not a law firm and +does not provide legal services or legal advice. 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For +the avoidance of doubt, this paragraph does not form part of the +public licenses. + +Creative Commons may be contacted at creativecommons.org. diff --git a/data/docs/Makefile b/data/docs/Makefile new file mode 100644 index 0000000000000000000000000000000000000000..d0c3cbf1020d5c292abdedf27627c6abe25e2293 --- /dev/null +++ b/data/docs/Makefile @@ -0,0 +1,20 @@ +# Minimal makefile for Sphinx documentation +# + +# You can set these variables from the command line, and also +# from the environment for the first two. +SPHINXOPTS ?= +SPHINXBUILD ?= sphinx-build +SOURCEDIR = source +BUILDDIR = build + +# Put it first so that "make" without argument is like "make help". +help: + @$(SPHINXBUILD) -M help "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O) + +.PHONY: help Makefile + +# Catch-all target: route all unknown targets to Sphinx using the new +# "make mode" option. $(O) is meant as a shortcut for $(SPHINXOPTS). +%: Makefile + @$(SPHINXBUILD) -M $@ "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O) diff --git a/data/docs/make.bat b/data/docs/make.bat new file mode 100644 index 0000000000000000000000000000000000000000..6fcf05b4b76f8b9774c317ac8ada402f8a7087de --- /dev/null +++ b/data/docs/make.bat @@ -0,0 +1,35 @@ +@ECHO OFF + +pushd %~dp0 + +REM Command file for Sphinx documentation + +if "%SPHINXBUILD%" == "" ( + set SPHINXBUILD=sphinx-build +) +set SOURCEDIR=source +set BUILDDIR=build + +if "%1" == "" goto help + +%SPHINXBUILD% >NUL 2>NUL +if errorlevel 9009 ( + echo. + echo.The 'sphinx-build' command was not found. Make sure you have Sphinx + echo.installed, then set the SPHINXBUILD environment variable to point + echo.to the full path of the 'sphinx-build' executable. Alternatively you + echo.may add the Sphinx directory to PATH. + echo. + echo.If you don't have Sphinx installed, grab it from + echo.https://www.sphinx-doc.org/ + exit /b 1 +) + +%SPHINXBUILD% -M %1 %SOURCEDIR% %BUILDDIR% %SPHINXOPTS% %O% +goto end + +:help +%SPHINXBUILD% -M help %SOURCEDIR% %BUILDDIR% %SPHINXOPTS% %O% + +:end +popd diff --git a/data/docs/requirements.txt b/data/docs/requirements.txt new file mode 100644 index 0000000000000000000000000000000000000000..c0dcbd81517bcd0e6bccb2e691350147afda7ad6 --- /dev/null +++ b/data/docs/requirements.txt @@ -0,0 +1,6 @@ +sphinx>=4.4.0 +sphinx_rtd_theme>=1.0.0 +sphinx_autodoc_defaultargs>=0.1.2 +sphinx_subfigure>=0.2.4 + +. diff --git a/data/docs/source/api/config.rst b/data/docs/source/api/config.rst new file mode 100644 index 0000000000000000000000000000000000000000..b6bcf351e21bc9e42c840b4d6e7b1391c480e6c1 --- /dev/null +++ b/data/docs/source/api/config.rst @@ -0,0 +1,10 @@ +.. _varipeps_config: + +.. currentmodule:: varipeps.config + +Config of variPEPS module (:mod:`varipeps.config`) +================================================== + +.. automodule:: varipeps.config + :members: + :show-inheritance: diff --git a/data/docs/source/api/contractions/apply.rst b/data/docs/source/api/contractions/apply.rst new file mode 100644 index 0000000000000000000000000000000000000000..087a6b6c70a25064a78d87f9baf64a88ab6e6472 --- /dev/null +++ b/data/docs/source/api/contractions/apply.rst @@ -0,0 +1,8 @@ +.. _varipeps_contractions_apply: + +.. currentmodule:: varipeps.contractions + +Apply a contraction (:func:`varipeps.contractions.apply_contraction`) +===================================================================== + +.. autofunction:: apply_contraction diff --git a/data/docs/source/api/contractions/definitions.rst b/data/docs/source/api/contractions/definitions.rst new file mode 100644 index 0000000000000000000000000000000000000000..73668dbecc6d2ba0fb4a46b70a8d38fdbc88bd96 --- /dev/null +++ b/data/docs/source/api/contractions/definitions.rst @@ -0,0 +1,11 @@ +.. _varipeps_contractions_definitions: + +.. currentmodule:: varipeps.contractions + +Definitions for contractions (:class:`varipeps.contractions.Definitions`) +========================================================================= + +.. autoclass:: Definitions + :members: + :undoc-members: + :show-inheritance: diff --git a/data/docs/source/api/contractions/index.rst b/data/docs/source/api/contractions/index.rst new file mode 100644 index 0000000000000000000000000000000000000000..9cd9a67f0373cc49a21dcc9b54dd5f0135aef92f --- /dev/null +++ b/data/docs/source/api/contractions/index.rst @@ -0,0 +1,20 @@ +.. _varipeps_contractions: + +.. py:module:: varipeps.contractions + +.. currentmodule:: varipeps.contractions + +Contractions definitions and helper methods (:mod:`varipeps.contractions`) +========================================================================== + +.. toctree:: + :maxdepth: 2 + + definitions + apply + +.. automodule:: varipeps.contractions + :members: + :undoc-members: + :show-inheritance: + :noindex: diff --git a/data/docs/source/api/ctmrg/absorption.rst b/data/docs/source/api/ctmrg/absorption.rst new file mode 100644 index 0000000000000000000000000000000000000000..dc76ee2561598f855a3fd69850fbdb1647b0d3fe --- /dev/null +++ b/data/docs/source/api/ctmrg/absorption.rst @@ -0,0 +1,13 @@ +.. _varipeps_ctmrg_absorption: + +.. module:: varipeps.ctmrg.absorption + +.. currentmodule:: varipeps.ctmrg.absorption + +Calculate the new CTMRG tensors for a single step (:mod:`varipeps.ctmrg.absorption`) +==================================================================================== + +.. automodule:: varipeps.ctmrg.absorption + :members: + :show-inheritance: + :noindex: diff --git a/data/docs/source/api/ctmrg/index.rst b/data/docs/source/api/ctmrg/index.rst new file mode 100644 index 0000000000000000000000000000000000000000..8ced47205bba548017179199ffa9b531dc3a8b85 --- /dev/null +++ b/data/docs/source/api/ctmrg/index.rst @@ -0,0 +1,21 @@ +.. _varipeps_ctmrg: + +.. py:module:: varipeps.ctmrg + +.. currentmodule:: varipeps.ctmrg + +CTMRG method (:mod:`varipeps.ctmrg`) +==================================== + +.. toctree:: + :maxdepth: 2 + + absorption + projectors + routine + +.. automodule:: varipeps.ctmrg + :members: + :undoc-members: + :show-inheritance: + :noindex: diff --git a/data/docs/source/api/ctmrg/projectors.rst b/data/docs/source/api/ctmrg/projectors.rst new file mode 100644 index 0000000000000000000000000000000000000000..04eaeda912d0ee9a35f4ada3e441fdc0794a3241 --- /dev/null +++ b/data/docs/source/api/ctmrg/projectors.rst @@ -0,0 +1,14 @@ +.. _varipeps_ctmrg_projectors: + +.. module:: varipeps.ctmrg.projectors + +.. currentmodule:: varipeps.ctmrg.projectors + +Calculation of CTMRG projectors (:mod:`varipeps.ctmrg.projectors`) +================================================================== + +.. automodule:: varipeps.ctmrg.projectors + :members: + :undoc-members: + :show-inheritance: + :noindex: diff --git a/data/docs/source/api/ctmrg/routine.rst b/data/docs/source/api/ctmrg/routine.rst new file mode 100644 index 0000000000000000000000000000000000000000..095c8a1f43702b944adc10a69e74a6a8ed2f2b05 --- /dev/null +++ b/data/docs/source/api/ctmrg/routine.rst @@ -0,0 +1,10 @@ +.. _varipeps_ctmrg_routine: + +.. currentmodule:: varipeps.ctmrg + +Calculate the new converged CTMRG tensors (:func:`varipeps.ctmrg.calc_ctmrg_env` and :func:`varipeps.ctmrg.calc_ctmrg_env_custom_rule`) +======================================================================================================================================= + +.. autofunction:: calc_ctmrg_env + +.. autofunction:: calc_ctmrg_env_custom_rule diff --git a/data/docs/source/api/expectation/four_sites.rst b/data/docs/source/api/expectation/four_sites.rst new file mode 100644 index 0000000000000000000000000000000000000000..0e7c861d02ebdcfb6ce6cd7323c514823235c06f --- /dev/null +++ b/data/docs/source/api/expectation/four_sites.rst @@ -0,0 +1,12 @@ +.. _varipeps_expectation_four_sites: + +.. currentmodule:: varipeps.expectation.four_sites + +Calculation of four sites expectation values +============================================ + +.. automodule:: varipeps.expectation.four_sites + :members: + :undoc-members: + :show-inheritance: + :special-members: __call__ diff --git a/data/docs/source/api/expectation/index.rst b/data/docs/source/api/expectation/index.rst new file mode 100644 index 0000000000000000000000000000000000000000..375ae65701aae1be68f4a4aaff54d6e8bdb28c91 --- /dev/null +++ b/data/docs/source/api/expectation/index.rst @@ -0,0 +1,24 @@ +.. _varipeps_expectation: + +.. py:module:: varipeps.expectation + +.. currentmodule:: varipeps.expectation + +Calculation of expectation values (:mod:`varipeps.expectation`) +=============================================================== + +.. toctree:: + :maxdepth: 2 + + model + one_site + two_sites + three_sites + four_sites + spiral_helpers + +.. automodule:: varipeps.expectation + :members: + :undoc-members: + :show-inheritance: + :noindex: diff --git a/data/docs/source/api/expectation/model.rst b/data/docs/source/api/expectation/model.rst new file mode 100644 index 0000000000000000000000000000000000000000..81af577f223a5192ff8c5fb9c024946a949a00ed --- /dev/null +++ b/data/docs/source/api/expectation/model.rst @@ -0,0 +1,12 @@ +.. _varipeps_expectation_model: + +.. currentmodule:: varipeps.expectation.model + +Model of general expectation value calculation +============================================== + +.. automodule:: varipeps.expectation.model + :members: + :undoc-members: + :show-inheritance: + :special-members: __call__ diff --git a/data/docs/source/api/expectation/one_site.rst b/data/docs/source/api/expectation/one_site.rst new file mode 100644 index 0000000000000000000000000000000000000000..2acb5e4d7e4e7c958b267fc36989d7a41f60c8a9 --- /dev/null +++ b/data/docs/source/api/expectation/one_site.rst @@ -0,0 +1,12 @@ +.. _varipeps_expectation_one_site: + +.. currentmodule:: varipeps.expectation.one_site + +Calculation of one site expectation values +========================================== + +.. automodule:: varipeps.expectation.one_site + :members: + :undoc-members: + :show-inheritance: + :special-members: __call__ diff --git a/data/docs/source/api/expectation/spiral_helpers.rst b/data/docs/source/api/expectation/spiral_helpers.rst new file mode 100644 index 0000000000000000000000000000000000000000..ad5e187d691e16a03de3fa6b1ec42a1e3f4fb05d --- /dev/null +++ b/data/docs/source/api/expectation/spiral_helpers.rst @@ -0,0 +1,12 @@ +.. _varipeps_expectation_spiral_helpers: + +.. currentmodule:: varipeps.expectation.spiral_helpers + +Helper functions for spiral iPEPS ansatz +======================================== + +.. automodule:: varipeps.expectation.spiral_helpers + :members: + :undoc-members: + :show-inheritance: + :special-members: __call__ diff --git a/data/docs/source/api/expectation/three_sites.rst b/data/docs/source/api/expectation/three_sites.rst new file mode 100644 index 0000000000000000000000000000000000000000..8788775b429deaf55139f65011cfb57a04142676 --- /dev/null +++ b/data/docs/source/api/expectation/three_sites.rst @@ -0,0 +1,12 @@ +.. _varipeps_expectation_three_sites: + +.. currentmodule:: varipeps.expectation.three_sites + +Calculation of three sites expectation values +============================================= + +.. automodule:: varipeps.expectation.three_sites + :members: + :undoc-members: + :show-inheritance: + :special-members: __call__ diff --git a/data/docs/source/api/expectation/two_sites.rst b/data/docs/source/api/expectation/two_sites.rst new file mode 100644 index 0000000000000000000000000000000000000000..ead32ffd183020ba43e4c4119a21edb457e3898f --- /dev/null +++ b/data/docs/source/api/expectation/two_sites.rst @@ -0,0 +1,12 @@ +.. _varipeps_expectation_two_sites: + +.. currentmodule:: varipeps.expectation.two_sites + +Calculation of two sites expectation values +=========================================== + +.. automodule:: varipeps.expectation.two_sites + :members: + :undoc-members: + :show-inheritance: + :special-members: __call__ diff --git a/data/docs/source/api/index.rst b/data/docs/source/api/index.rst new file mode 100644 index 0000000000000000000000000000000000000000..f30b719937f77f7611699d34a33de9f5072e86c8 --- /dev/null +++ b/data/docs/source/api/index.rst @@ -0,0 +1,25 @@ +.. _api: + +.. module:: varipeps + +###################### +variPEPS API reference +###################### + +This reference documents the public API of the :mod:`varipeps` module. The API +documentation is automatically generated from the source code of the +:obj:`varipeps` library and is therefore licensed under the +:ref:`license_gpl_3`. + +.. toctree:: + :maxdepth: 2 + + config + contractions/index + ctmrg/index + expectation/index + mapping/index + optimization/index + peps/index + typing + utils/index diff --git a/data/docs/source/api/mapping/florett_pentagon.rst b/data/docs/source/api/mapping/florett_pentagon.rst new file mode 100644 index 0000000000000000000000000000000000000000..fc3b65c30300b561ded26ab0c1bd1e278240b48a --- /dev/null +++ b/data/docs/source/api/mapping/florett_pentagon.rst @@ -0,0 +1,12 @@ +.. _varipeps_mapping_florett_pentagon: + +.. currentmodule:: varipeps.mapping.florett_pentagon + +Mapping of Floret-Pentagon structures (:mod:`varipeps.mapping.florett_pentagon`) +================================================================================ + +.. automodule:: varipeps.mapping.florett_pentagon + :members: + :undoc-members: + :show-inheritance: + :special-members: __call__ diff --git a/data/docs/source/api/mapping/honeycomb.rst b/data/docs/source/api/mapping/honeycomb.rst new file mode 100644 index 0000000000000000000000000000000000000000..36d2ea54e7dbfc329f3183b85d80e1b63d7eada6 --- /dev/null +++ b/data/docs/source/api/mapping/honeycomb.rst @@ -0,0 +1,12 @@ +.. _varipeps_mapping_honeycomb: + +.. currentmodule:: varipeps.mapping.honeycomb + +Mapping of Honeycomb structures (:mod:`varipeps.mapping.honeycomb`) +=================================================================== + +.. automodule:: varipeps.mapping.honeycomb + :members: + :undoc-members: + :show-inheritance: + :special-members: __call__ diff --git a/data/docs/source/api/mapping/index.rst b/data/docs/source/api/mapping/index.rst new file mode 100644 index 0000000000000000000000000000000000000000..07ccd8103e965acd13f3333e7df87b6f450a3665 --- /dev/null +++ b/data/docs/source/api/mapping/index.rst @@ -0,0 +1,24 @@ +.. _varipeps_mapping: + +.. py:module:: varipeps.mapping + +.. currentmodule:: varipeps.mapping + +Mapping of other structures to PEPS unitcells (:mod:`varipeps.mapping`) +======================================================================= + +.. toctree:: + :maxdepth: 2 + + florett_pentagon + honeycomb + kagome + maple_leaf + square_kagome + triangular + +.. automodule:: varipeps.mapping + :members: + :undoc-members: + :show-inheritance: + :noindex: diff --git a/data/docs/source/api/mapping/kagome.rst b/data/docs/source/api/mapping/kagome.rst new file mode 100644 index 0000000000000000000000000000000000000000..2c4de50a9ea80070b61b9d79c2f3f4719302ee51 --- /dev/null +++ b/data/docs/source/api/mapping/kagome.rst @@ -0,0 +1,12 @@ +.. _varipeps_mapping_kagome: + +.. currentmodule:: varipeps.mapping.kagome + +Mapping of Kagome structures (:mod:`varipeps.mapping.kagome`) +============================================================= + +.. automodule:: varipeps.mapping.kagome + :members: + :undoc-members: + :show-inheritance: + :special-members: __call__ diff --git a/data/docs/source/api/mapping/maple_leaf.rst b/data/docs/source/api/mapping/maple_leaf.rst new file mode 100644 index 0000000000000000000000000000000000000000..29fc83649bc25300c42f2e5d4f23b6bfd6f73c99 --- /dev/null +++ b/data/docs/source/api/mapping/maple_leaf.rst @@ -0,0 +1,12 @@ +.. _varipeps_mapping_maple_leaf: + +.. currentmodule:: varipeps.mapping.maple_leaf + +Mapping of Maple leaf structures (:mod:`varipeps.mapping.maple_leaf`) +===================================================================== + +.. automodule:: varipeps.mapping.maple_leaf + :members: + :undoc-members: + :show-inheritance: + :special-members: __call__ diff --git a/data/docs/source/api/mapping/square_kagome.rst b/data/docs/source/api/mapping/square_kagome.rst new file mode 100644 index 0000000000000000000000000000000000000000..442a5cb31c36538b90a1950865c6838027e40fc5 --- /dev/null +++ b/data/docs/source/api/mapping/square_kagome.rst @@ -0,0 +1,12 @@ +.. _varipeps_mapping_square_kagome: + +.. currentmodule:: varipeps.mapping.square_kagome + +Mapping of Square-Kagome structures (:mod:`varipeps.mapping.square_kagome`) +=========================================================================== + +.. automodule:: varipeps.mapping.square_kagome + :members: + :undoc-members: + :show-inheritance: + :special-members: __call__ diff --git a/data/docs/source/api/mapping/triangular.rst b/data/docs/source/api/mapping/triangular.rst new file mode 100644 index 0000000000000000000000000000000000000000..25cc2c67031f6e64d8d1b952378fb137be1cd902 --- /dev/null +++ b/data/docs/source/api/mapping/triangular.rst @@ -0,0 +1,12 @@ +.. _varipeps_mapping_triangular: + +.. currentmodule:: varipeps.mapping.triangular + +Mapping of Triangular structures (:mod:`varipeps.mapping.triangular`) +===================================================================== + +.. automodule:: varipeps.mapping.triangular + :members: + :undoc-members: + :show-inheritance: + :special-members: __call__ diff --git a/data/docs/source/api/optimization/basinhopping.rst b/data/docs/source/api/optimization/basinhopping.rst new file mode 100644 index 0000000000000000000000000000000000000000..9793894836ee8109040cfa2be6b8053ef62df8f2 --- /dev/null +++ b/data/docs/source/api/optimization/basinhopping.rst @@ -0,0 +1,11 @@ +.. _varipeps_optimization_basinhopping: + +.. currentmodule:: varipeps.optimization.basinhopping + +Implementation of the basinhopping optimizer for the PEPS model (:mod:`varipeps.optimization.basinhopping`) +=========================================================================================================== + +.. automodule:: varipeps.optimization.basinhopping + :members: + :undoc-members: + :show-inheritance: diff --git a/data/docs/source/api/optimization/index.rst b/data/docs/source/api/optimization/index.rst new file mode 100644 index 0000000000000000000000000000000000000000..ae3101f5d019e5d35f2b9438dd2534d6f4236260 --- /dev/null +++ b/data/docs/source/api/optimization/index.rst @@ -0,0 +1,22 @@ +.. _varipeps_optimization: + +.. py:module:: varipeps.optimization + +.. currentmodule:: varipeps.optimization + +Variational optimizer for the PEPS network (:mod:`varipeps.optimization`) +========================================================================= + +.. toctree:: + :maxdepth: 2 + + basinhopping + inner_function + line_search + optimizer + +.. automodule:: varipeps.optimization + :members: + :undoc-members: + :show-inheritance: + :noindex: diff --git a/data/docs/source/api/optimization/inner_function.rst b/data/docs/source/api/optimization/inner_function.rst new file mode 100644 index 0000000000000000000000000000000000000000..581a9ffaef58057f48f330587c4b7e86736ada72 --- /dev/null +++ b/data/docs/source/api/optimization/inner_function.rst @@ -0,0 +1,11 @@ +.. _varipeps_optimization_inner_function: + +.. currentmodule:: varipeps.optimization.inner_function + +Methods to calculate the CTRMG env and expectation value along with the gradient (:mod:`varipeps.optimization.inner_function`) +============================================================================================================================== + +.. automodule:: varipeps.optimization.inner_function + :members: + :undoc-members: + :show-inheritance: diff --git a/data/docs/source/api/optimization/line_search.rst b/data/docs/source/api/optimization/line_search.rst new file mode 100644 index 0000000000000000000000000000000000000000..73394147470c71dddd03820c253606f693b3cf8d --- /dev/null +++ b/data/docs/source/api/optimization/line_search.rst @@ -0,0 +1,11 @@ +.. _varipeps_optimization_line_search: + +.. currentmodule:: varipeps.optimization.line_search + +Implementation of line search methods for the CTMRG variational optimization (:mod:`varipeps.optimization.line_search`) +======================================================================================================================= + +.. automodule:: varipeps.optimization.line_search + :members: + :undoc-members: + :show-inheritance: diff --git a/data/docs/source/api/optimization/optimizer.rst b/data/docs/source/api/optimization/optimizer.rst new file mode 100644 index 0000000000000000000000000000000000000000..7b3f5cbaecf6a7c708ad604acb24f0d5ab923bb2 --- /dev/null +++ b/data/docs/source/api/optimization/optimizer.rst @@ -0,0 +1,11 @@ +.. _varipeps_optimization_optimizer: + +.. currentmodule:: varipeps.optimization.optimizer + +Implementation of the variational optimizer for the PEPS model (:mod:`varipeps.optimization.optimizer`) +======================================================================================================= + +.. automodule:: varipeps.optimization.optimizer + :members: + :undoc-members: + :show-inheritance: diff --git a/data/docs/source/api/peps/index.rst b/data/docs/source/api/peps/index.rst new file mode 100644 index 0000000000000000000000000000000000000000..9d9d31e6c81997fb582d6e29840876b871705c6b --- /dev/null +++ b/data/docs/source/api/peps/index.rst @@ -0,0 +1,14 @@ +.. _varipeps_peps: + +.. py:module:: varipeps.peps + +.. currentmodule:: varipeps.peps + +Implementation of PEPS structure (:mod:`varipeps.peps`) +======================================================= + +.. toctree:: + :maxdepth: 2 + + tensor + unitcell diff --git a/data/docs/source/api/peps/tensor.rst b/data/docs/source/api/peps/tensor.rst new file mode 100644 index 0000000000000000000000000000000000000000..6fa3f7b34c5e9b49afd28967c82f525aeaebf9f3 --- /dev/null +++ b/data/docs/source/api/peps/tensor.rst @@ -0,0 +1,12 @@ +.. _varipeps_peps_tensor: + +.. currentmodule:: varipeps.peps + +Single PEPS tensor (:class:`varipeps.peps.PEPS_Tensor`) +======================================================= + +.. autoclass:: PEPS_Tensor + :members: + :undoc-members: + :show-inheritance: + :special-members: __add__ diff --git a/data/docs/source/api/peps/unitcell.rst b/data/docs/source/api/peps/unitcell.rst new file mode 100644 index 0000000000000000000000000000000000000000..b50edc651299434da7f82fee62a908ac1387ed1d --- /dev/null +++ b/data/docs/source/api/peps/unitcell.rst @@ -0,0 +1,12 @@ +.. _varipeps_peps_unit_cell: + +.. currentmodule:: varipeps.peps + +PEPS Unit cell (:class:`varipeps.peps.PEPS_Unit_Cell`) +====================================================== + +.. autoclass:: PEPS_Unit_Cell + :members: + :undoc-members: + :special-members: __getitem__ + :show-inheritance: diff --git a/data/docs/source/api/typing.rst b/data/docs/source/api/typing.rst new file mode 100644 index 0000000000000000000000000000000000000000..1bef3e1fc61d083edfb6adba8b7ac351844cda22 --- /dev/null +++ b/data/docs/source/api/typing.rst @@ -0,0 +1,14 @@ +.. _varipeps_typing: + +.. py:module:: varipeps.typing + +.. currentmodule:: varipeps.typing + +Typing helper (:mod:`varipeps.typing`) +====================================== + +.. automodule:: varipeps.typing + :members: + :undoc-members: + :show-inheritance: + :noindex: diff --git a/data/docs/source/api/utils/debug_print.rst b/data/docs/source/api/utils/debug_print.rst new file mode 100644 index 0000000000000000000000000000000000000000..610b2df672a331afbb774dc8312325ac77d4c29f --- /dev/null +++ b/data/docs/source/api/utils/debug_print.rst @@ -0,0 +1,11 @@ +.. _varipeps_utils_debug_print: + +.. currentmodule:: varipeps.utils.debug_print + +Debugging output helpers (:mod:`varipeps.utils.debug_print`) +============================================================ + +.. automodule:: varipeps.utils.debug_print + :members: + :undoc-members: + :show-inheritance: diff --git a/data/docs/source/api/utils/index.rst b/data/docs/source/api/utils/index.rst new file mode 100644 index 0000000000000000000000000000000000000000..c368f7ff108296214ac5a99565ccf7989f9be486 --- /dev/null +++ b/data/docs/source/api/utils/index.rst @@ -0,0 +1,23 @@ +.. _varipeps_utils: + +.. py:module:: varipeps.utils + +.. currentmodule:: varipeps.utils + +Utility functions (:mod:`varipeps.utils`) +========================================= + +.. toctree:: + :maxdepth: 2 + + debug_print + periodic_indices + projector_dict + random + svd + +.. automodule:: varipeps.utils + :members: + :undoc-members: + :show-inheritance: + :noindex: diff --git a/data/docs/source/api/utils/periodic_indices.rst b/data/docs/source/api/utils/periodic_indices.rst new file mode 100644 index 0000000000000000000000000000000000000000..b055e60ec67c9a76941d9d8b1b758b16d5e06693 --- /dev/null +++ b/data/docs/source/api/utils/periodic_indices.rst @@ -0,0 +1,11 @@ +.. _varipeps_utils_periodic_indices: + +.. currentmodule:: varipeps.utils.periodic_indices + +Helper to calculate perodic indices (:mod:`varipeps.utils.periodic_indices`) +============================================================================ + +.. automodule:: varipeps.utils.periodic_indices + :members: + :undoc-members: + :show-inheritance: diff --git a/data/docs/source/api/utils/projector_dict.rst b/data/docs/source/api/utils/projector_dict.rst new file mode 100644 index 0000000000000000000000000000000000000000..c7d3d38051cb81742cf90625d851115a6a8c5810 --- /dev/null +++ b/data/docs/source/api/utils/projector_dict.rst @@ -0,0 +1,11 @@ +.. _varipeps_utils_projector_dict: + +.. currentmodule:: varipeps.utils.projector_dict + +CTM projector management helpers (:mod:`varipeps.utils.projector_dict`) +======================================================================= + +.. automodule:: varipeps.utils.projector_dict + :members: + :undoc-members: + :show-inheritance: diff --git a/data/docs/source/api/utils/random.rst b/data/docs/source/api/utils/random.rst new file mode 100644 index 0000000000000000000000000000000000000000..88e7e26657340391a1cc6613f5e514ff7d667cd1 --- /dev/null +++ b/data/docs/source/api/utils/random.rst @@ -0,0 +1,14 @@ +.. _varipeps_utils_random: + +.. py:module:: varipeps.utils.random + +.. currentmodule:: varipeps.utils.random + +Random number helpers (:mod:`varipeps.utils.random`) +==================================================== + +.. automodule:: varipeps.utils.random + :members: + :undoc-members: + :show-inheritance: + :noindex: diff --git a/data/docs/source/api/utils/svd.rst b/data/docs/source/api/utils/svd.rst new file mode 100644 index 0000000000000000000000000000000000000000..654653e94d7efe308ac75ff4b06ac4477788f87a --- /dev/null +++ b/data/docs/source/api/utils/svd.rst @@ -0,0 +1,11 @@ +.. _varipeps_utils_svd: + +.. currentmodule:: varipeps.utils.svd + +SVD helpers (:mod:`varipeps.utils.svd`) +======================================= + +.. automodule:: varipeps.utils.svd + :members: + :undoc-members: + :show-inheritance: diff --git a/data/docs/source/conf.py b/data/docs/source/conf.py new file mode 100644 index 0000000000000000000000000000000000000000..4f79a38bd529d509e9d30e1a5e701f3d1d7bb00b --- /dev/null +++ b/data/docs/source/conf.py @@ -0,0 +1,159 @@ +# Configuration file for the Sphinx documentation builder. +# +# This file only contains a selection of the most common options. For a full +# list see the documentation: +# https://www.sphinx-doc.org/en/master/usage/configuration.html + +# -- Path setup -------------------------------------------------------------- + +# If extensions (or modules to document with autodoc) are in another directory, +# add these directories to sys.path here. If the directory is relative to the +# documentation root, use os.path.abspath to make it absolute, like shown here. +# +import os +import sys +import importlib +import importlib.metadata +import inspect + +sys.path.insert(0, os.path.abspath("..")) + + +# -- Project information ----------------------------------------------------- + +project = "varipeps" +copyright = "2021-2026, Jan Naumann, Philipp Schmoll, Roberto Losada, Frederik Wilde, Finn Krein" +author = "Jan Naumann, Philipp Schmoll, Roberto Losada, Frederik Wilde, Finn Krein" + +# The full version, including alpha/beta/rc tags +release = importlib.metadata.version("varipeps") + + +# -- General configuration --------------------------------------------------- + +# Add any Sphinx extension module names here, as strings. They can be +# extensions coming with Sphinx (named 'sphinx.ext.*') or your custom +# ones. +extensions = [ + "sphinx.ext.autodoc", + "sphinx.ext.autosummary", + "sphinx.ext.linkcode", + "sphinx.ext.mathjax", + "sphinx.ext.napoleon", + "sphinx.ext.intersphinx", + "sphinx_autodoc_defaultargs", + "sphinx_subfigure", +] + +napoleon_include_private_with_doc = True +napoleon_preprocess_types = False + +autodoc_type_aliases = { + "T_PEPS_Unit_Cell": "PEPS_Unit_Cell", + "T_PEPS_Tensor": "PEPS_Tensor", + "PEPS_Unit_Cell.Unit_Cell_Data": "varipeps.peps.PEPS_Unit_Cell.Unit_Cell_Data", + "jax._src.numpy.lax_numpy.ndarray": "jax.numpy.ndarray", + "h5py._hl.group.Group": "h5py.Group", +} + +# autodoc_mock_imports = ["jax"] + +intersphinx_mapping = { + "python": ("https://docs.python.org/3", None), + "jax": ("https://jax.readthedocs.io/en/latest/", None), + "numpy": ("https://numpy.org/doc/stable/", None), + "scipy": ("https://docs.scipy.org/doc/scipy/reference/", None), + "h5py": ("https://docs.h5py.org/en/stable/", None), +} + +# Add any paths that contain templates here, relative to this directory. +templates_path = ["_templates"] + +# List of patterns, relative to source directory, that match files and +# directories to ignore when looking for source files. +# This pattern also affects html_static_path and html_extra_path. +exclude_patterns = [] + +from varipeps import git_commit, git_tag + +code_url = "https://github.com/variPEPS/variPEPS_Python/blob/{blob}" + +if git_tag is not None: + code_url = code_url.format(blob=git_tag) +elif git_commit is not None: + code_url = code_url.format(blob=git_commit) +else: + code_url = code_url.format(blob=release) + + +def linkcode_resolve(domain, info): + # Code adapted from function in websockets module + # https://github.com/python-websockets/websockets/blob/e217458ef8b692e45ca6f66c5aeb7fad0aee97ee/docs/conf.py + + if domain != "py": + return None + if not info["module"]: + return None + + mod = importlib.import_module(info["module"]) + if "." in info["fullname"]: + objname_parts = info["fullname"].split(".") + + obj = getattr(mod, objname_parts[0]) + + for name in objname_parts[1:-1]: + obj = getattr(obj, name) + + attrname = objname_parts[-1] + + try: + # object is a method of a class + obj = getattr(obj, attrname) + except AttributeError: + # object is an attribute of a class + return None + else: + obj = getattr(mod, info["fullname"]) + + try: + filename = inspect.getsourcefile(obj) + lines = inspect.getsourcelines(obj) + except (TypeError, OSError): + # e.g. object is a typing.Union + return None + + filename = os.path.relpath(filename, os.path.abspath("../..")) + + if not filename.startswith("varipeps"): + # e.g. object is a typing.NewType + return None + start, end = lines[1], lines[1] + len(lines[0]) - 1 + + return f"{code_url}/{filename}#L{start}-L{end}" + + +# -- Options for HTML output ------------------------------------------------- + +# The theme to use for HTML and HTML Help pages. See the documentation for +# a list of builtin themes. +# +html_theme = "sphinx_rtd_theme" + +# Add any paths that contain custom static files (such as style sheets) here, +# relative to this directory. They are copied after the builtin static files, +# so a file named "default.css" will overwrite the builtin "default.css". +html_static_path = ["_static"] + +html_logo = "images/logo.svg" +html_favicon = "images/favicon/favicon.svg" + +html_theme_options = { + 'logo_only': True, +} + +rst_prolog = """ +.. |default| raw:: html + +
Default:""" + +numfig = True diff --git a/data/docs/source/examples/heisenberg_afm_square.rst b/data/docs/source/examples/heisenberg_afm_square.rst new file mode 100644 index 0000000000000000000000000000000000000000..5752342709fb5c4078cac37e6e8c443cd8134c2f --- /dev/null +++ b/data/docs/source/examples/heisenberg_afm_square.rst @@ -0,0 +1,235 @@ +.. _examples_heisenberg_afm_square: + +Heisenberg antiferromagnet on the square lattice +------------------------------------------------ + +.. figure:: /images/square_lattice.* + :align: center + :width: 60% + :alt: Two dimensional square lattice with red links indicating horizontal and + blue links indicating vertical interactions. + + Two dimensional square lattice + +The Hamiltonian for the Heisenberg antiferromagnet with constant exchange +interaction strength :math:`J>0` is defined as: + +.. math:: + + H = J \sum_{\langle i j \rangle} \vec{S}_i \vec{S}_j , + +where :math:`\langle i j \rangle` denotes the sum over all nearest neighbors in +the lattice. + +Our aim is now to find the ground state of the model using the variational iPEPS +code of the variPEPS library. + +Loading of relevant Python modules +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +.. code-block:: python + + import varipeps + import jax + import jax.numpy as jnp + +First of all we have to load the relevant Python modules for our simulation. The +:obj:`varipeps` module includes the full library to perform the variational +optimization. Internally it is based on the :obj:`jax` framework and its +:obj:`numpy`-like interface to execute the calculations. Since we will need +arrays to define for example the Hamiltonian, we load this numpy +interface as well. + +variPEPS config settings +^^^^^^^^^^^^^^^^^^^^^^^^ + +.. code-block:: python + + # Config Setting + + ## Set maximal steps for the CTMRG routine + varipeps.config.ctmrg_max_steps = 100 + ## Set convergence threshold for the CTMRG routine + varipeps.config.ctmrg_convergence_eps = 1e-7 + ## Select the method used to calculate the (full) projectors in the CTMRG routine + varipeps.config.ctmrg_full_projector_method = ( + varipeps.config.Projector_Method.FISHMAN + ) + ## Enable dynamic increase of CTMRG environment bond dimension + varipeps.config.ctmrg_heuristic_increase_chi = True + ## Increase CTMRG enviroment bond dimension if truncation error exceeds this value + varipeps.config.ctmrg_heuristic_increase_chi_threshold = 1e-4 + + ## Set maximal steps for the fix point routine in the gradient calculation + varipeps.config.ad_custom_max_steps = 100 + ## Set convergence threshold for the fix point routine in the gradient calculation + varipeps.config.ad_custom_convergence_eps = 5e-8 + + ## Enable/Disable printing of the convergence of the single CTMRG/gradient fix point steps. + ## Useful to enable this during debugging, should be disabled for batch runs + varipeps.config.ctmrg_print_steps = True + varipeps.config.ad_custom_print_steps = False + + ## Select the method used to calculate the descent direction during optimization + varipeps.config.optimizer_method = varipeps.config.Optimizing_Methods.L_BFGS + ## Set maximal number of steps for the optimization routine + varipeps.config.optimizer_max_steps = 2000 + +The :obj:`varipeps` library allows to configure a large number of numerical +parameters to fine-tune the simulation. In this example we include several +options commonly used in an optimization run. For a detailed +description of the configurable options we refer to the API description of the +config class: :obj:`varipeps.config.VariPEPS_Config`. + +Model parameters +^^^^^^^^^^^^^^^^ + +.. code-block:: python + + # Set constants for the simulation + modelName = "HeisenbergModel" + # Interaction strength + J = 1 + # iPEPS bond dimension + chiB = 2 + # Physical dimension + p = 2 + # Maximal enviroment bond dimension + maxChi = 36 + # Start value for enviroment bond dimension + startChi = chiB**2 if chiB**2 < maxChi else maxChi + +In this block we define imporant parameters for the model we want to simulate, such as as the interaction strength, the physical dimension of our tensor network and the iPEPS bond dimension. In the last two lines the initial and the maximal enviroment bond dimension is defined. A feature of the variPEPS library is that it not only supports simulation at a fixed enviroment bond dimension, but also a heurisitic increase/decrease of the dimension up to a maximal value. The dynamic change is controlled by the truncation error in the CTMRG projector calculation (increase if the truncation errror becomes too large, decrease if it becomes insignificant). For example, in the config block above the parameter ``ctmrg_heuristic_increase_chi_threshold`` is set to the threshold at which to increase the refinement parameter. The maximal bond dimension ``maxChi`` ensures that the parameter does now grow unbounded, to the point where the memory and computational resources are exhausted. + +Constructing the Hamiltonian +^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +.. code-block:: python + + # define spin-1/2 matrices + Id = jnp.eye(2) + Sx = jnp.array([[0, 1], [1, 0]]) / 2 + Sy = jnp.array([[0, -1j], [1j, 0]]) / 2 + Sz = jnp.array([[1, 0], [0, -1]]) / 2 + + # construct Hamiltonian terms + hamiltonianGates = J * (jnp.kron(Sx, Sx) + jnp.kron(Sy, Sy) + jnp.kron(Sz, Sz)) + + # create function to compute expectation values for the square Heisenberg AFM + exp_func = varipeps.expectation.Two_Sites_Expectation_Value( + horizontal_gates=(hamiltonianGates,), + vertical_gates=(hamiltonianGates,), + ) + +Here the Hamiltonian is constructed for our model. The Heisenberg AFM on the +square lattice can be described by the sum of the spin-spin interactions on +the horizontal and vertical bonds. Since we assume a constant +interaction strength for all bonds in our example, the expectation value can be calculated by +the same two-site interaction gate applied in all nearest neighbor +directions. The expectation function ``exp_func`` is later used in the +optimization to calculate the energy expectation value, which in turn is used as cost function to obtain +the ground state. + +Initial unit cell construction +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +.. code-block:: python + + # Unit cell structure + structure = [[0, 1], [1, 0]] + +Here we define the unit cell structure which is used to simulate our model. In +this example we assume a +:math:`\scriptsize{\begin{matrix}A&B\\B&A\end{matrix}}`-structure, i.e. a two-site antiferromagnetic state. + +.. code-block:: python + + # Create random initialization for the iPEPS unit cell + unitcell = varipeps.peps.PEPS_Unit_Cell.random( + structure, # Unit cell structure + p, # Physical dimension + chiB, # iPEPS bond dimension + startChi, # Start value for enviroment bond dimension + float, # Data type for the tensors: `float` (real) or `complex` tensors + max_chi=maxChi, # Maximal enviroment bond dimension + ) + +Using the unit cell structure and the model parameter defined above, we can +generate an initial unit cell. Here we initialize the iPEPS tensors with random +numbers. Other ways to initialize the tensors are provided, for example loading results +from a simple update calculation. + +Run the optimization +^^^^^^^^^^^^^^^^^^^^ + +.. code-block:: python + + # Run optimization + result = varipeps.optimization.optimize_peps_network( + unitcell, + exp_func, + autosave_filename=f"data/autosave_square_chiB_{chiB:d}.hdf5", + ) + +This function call executes the main function of the library, the variational energy +optimization to obtain a good ground state candidate. The function offers several options +to customize the optimization for different iPEPS ansätze, such as the spiral iPEPS +approach. In our example, we only need to provide the initial unit cell, the function +for calculating the energy expectation value, and a file path for autosaving the +optimization process, enabling the restoration of interrupted simulations. + +Evaluate the results +^^^^^^^^^^^^^^^^^^^^ + +In this section we show some exemplary evaluation of the result of the optimization. + +.. code-block:: python + + # Calculate magnetic expectation values + Mag_Gates = [Sx, Sy, Sz] + + + def calc_magnetic(unitcell): + mag_result = [] + for ti, t in enumerate(unitcell.get_unique_tensors()): + r = varipeps.expectation.one_site.calc_one_site_multi_gates( + t.tensor, t, Mag_Gates + ) + mag_result += r + return mag_result + + + magnetic_exp_values = calc_magnetic(result.unitcell) + +We assume for our example that we are interested in the single-site spin +expectation values. These could be used to analyse the :math:`z`-magnetization +or the staggered magnetization of our model at/near the ground state. + +.. code-block:: python + + # Define some auxiliary data which should be stored along the final iPEPS unit cell + auxiliary_data = { + "best_energy": result.fun, + "best_run": result.best_run, + "magnetic_exp_values": magnetic_exp_values, + } + for k in sorted(result.max_trunc_error_list.keys()): + auxiliary_data[f"max_trunc_error_list_{k:d}"] = result.max_trunc_error_list[k] + auxiliary_data[f"step_energies_{k:d}"] = result.step_energies[k] + auxiliary_data[f"step_chi_{k:d}"] = result.step_chi[k] + auxiliary_data[f"step_conv_{k:d}"] = result.step_conv[k] + auxiliary_data[f"step_runtime_{k:d}"] = result.step_runtime[k] + + # save full iPEPS state + result.unitcell.save_to_file( + f"data/heisenberg_square_J_{J:d}_chiB_{chiB:d}_chiMax_{chiM:d}.hdf5", + auxiliary_data=auxiliary_data, + ) + +Finally, we want to save the unit cell with the optimized tensors to a file for +further analysis. The library allows to store the data directly into a +HDF5 file along with user-supplied auxiliary data. Here, for example, we not only +want to store the plain tensors but also the calculated energy, meta information +from the optimization run (e.g. energy per step or the runtime per step) and the +calculated magnetic expectation values. At a later examination of the results, +these data can be easily loaded along with the tensors of the tensor network. diff --git a/data/docs/source/examples/heisenberg_afm_triangular.rst b/data/docs/source/examples/heisenberg_afm_triangular.rst new file mode 100644 index 0000000000000000000000000000000000000000..0e934a6acadffe4b0355d4b4bf2295bbfac19470 --- /dev/null +++ b/data/docs/source/examples/heisenberg_afm_triangular.rst @@ -0,0 +1,280 @@ +.. _examples_heisenberg_afm_triangular: + +Heisenberg antiferromagnet on the triangular lattice +---------------------------------------------------- + +.. figure:: /images/triangular_lattice.* + :align: center + :width: 60% + :alt: Two dimensional triangular lattice with links indicating nearest neighbor + interactions. + + Two dimensional triangular lattice + +The Hamiltonian for the Heisenberg antiferromagnet with constant exchange +interaction strength :math:`J>0` is defined as: + +.. math:: + + H = J \sum_{\langle i j \rangle} \vec{S}_i \vec{S}_j , + +where :math:`\langle i j \rangle` denotes the sum over all nearest neighbors in +the lattice. + +Our aim is now to find the ground state of the model using the variational iPEPS +code of the variPEPS library. + +Loading of relevant Python modules +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +.. code-block:: python + + import varipeps + import jax + import jax.numpy as jnp + +First of all we have to load the relevant Python modules for our simulation. The +:obj:`varipeps` module includes the full library to perform the variational +optimization. Internally it is based on the :obj:`jax` framework and its +:obj:`numpy`-like interface to execute the calculations. Since we will need +arrays to define for example the Hamiltonian, we load this numpy interface as +well. + +variPEPS config settings +^^^^^^^^^^^^^^^^^^^^^^^^ + +.. code-block:: python + + # Config Setting + + ## Set maximal steps for the CTMRG routine + varipeps.config.ctmrg_max_steps = 100 + ## Set convergence threshold for the CTMRG routine + varipeps.config.ctmrg_convergence_eps = 1e-7 + ## Select the method used to calculate the (full) projectors in the CTMRG routine + varipeps.config.ctmrg_full_projector_method = ( + varipeps.config.Projector_Method.FISHMAN + ) + ## Enable dynamic increase of CTMRG environment bond dimension + varipeps.config.ctmrg_heuristic_increase_chi = True + ## Increase CTMRG enviroment bond dimension if truncation error exceeds this value + varipeps.config.ctmrg_heuristic_increase_chi_threshold = 1e-4 + + ## Set maximal steps for the fix point routine in the gradient calculation + varipeps.config.ad_custom_max_steps = 100 + ## Set convergence threshold for the fix point routine in the gradient calculation + varipeps.config.ad_custom_convergence_eps = 5e-8 + + ## Enable/Disable printing of the convergence of the single CTMRG/gradient fix point steps. + ## Useful to enable this during debugging, should be disabled for batch runs + varipeps.config.ctmrg_print_steps = True + varipeps.config.ad_custom_print_steps = False + + ## Select the method used to calculate the descent direction during optimization + varipeps.config.optimizer_method = varipeps.config.Optimizing_Methods.CG + ## Set maximal number of steps for the optimization routine + varipeps.config.optimizer_max_steps = 2000 + +The :obj:`varipeps` library allows to configure a large number of numerical +parameters to fine-tune the simulation. In this example we include several +options commonly used in an optimization run. For a detailed description of the +configurable options we refer to the API description of the config class: +:obj:`varipeps.config.VariPEPS_Config`. + +Model parameters +^^^^^^^^^^^^^^^^ + +.. code-block:: python + + # Set constants for the simulation + modelName = "HeisenbergModel" + # Interaction strength + J = 1 + # iPEPS bond dimension + chiB = 2 + # Physical dimension + p = 2 + # Maximal enviroment bond dimension + maxChi = 64 + # Start value for enviroment bond dimension + startChi = maxChi + +In this block we define imporant parameters for the model we want to simulate, +such as as the interaction strength, the physical dimension of our tensor +network and the iPEPS bond dimension. In the last two lines the initial and the +maximal enviroment bond dimension is defined. A feature of the variPEPS library +is that it not only supports simulation at a fixed enviroment bond dimension, +but also a heurisitic increase/decrease of the dimension up to a maximal +value. The dynamic change is controlled by the truncation error in the CTMRG +projector calculation (increase if the truncation error becomes too large, +decrease if it becomes insignificant). For example, in the config block above +the parameter ``ctmrg_heuristic_increase_chi_threshold`` is set to the threshold +at which to increase the refinement parameter. The maximal bond dimension +``maxChi`` ensures that the parameter does now grow unbounded, to the point +where the memory and computational resources are exhausted. + +For the triangular lattice Heisenberg AFM it is known that a quite large +environment bond dimension is needed such that we directly start the simulation +with the maximal allowed dimension to avoid unnecessary calculations. + +Constructing the Hamiltonian +^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +.. code-block:: python + + # define spin-1/2 matrices + Id = jnp.eye(2) + Sx = jnp.array([[0, 1], [1, 0]]) / 2 + Sy = jnp.array([[0, -1j], [1j, 0]]) / 2 + Sz = jnp.array([[1, 0], [0, -1]]) / 2 + + # construct Hamiltonian terms + hamiltonianGates = J * (jnp.kron(Sx, Sx) + jnp.kron(Sy, Sy) + jnp.kron(Sz, Sz)) + + # create function to compute expectation values for the square Heisenberg AFM + exp_func = ( + varipeps.expectation.triangular_two_sites.Triangular_Two_Sites_Expectation_Value( + horizontal_gates=(hamiltonianGates,), + vertical_gates=(hamiltonianGates,), + diagonal_gates=(hamiltonianGates,), + real_d=p, + is_spiral_peps=True, + spiral_unitary_operator=Sy, + ) + ) + +Here the Hamiltonian is constructed for our model. The Heisenberg AFM on the +triangular lattice can be described by the sum of the spin-spin interactions on +the horizontal, vertical and diagonal bonds. Since we assume a constant +interaction strength for all bonds in our example, the expectation value can be +calculated by the same two-site interaction gate applied in all nearest neighbor +directions. The expectation function ``exp_func`` is later used in the +optimization to calculate the energy expectation value, which in turn is used as +cost function to obtain the ground state. + +We use in this example the description of the model by the spiral-PEPS ansatz +(`Phys. Rev. Lett. 133, 176502 (2024) +`_). Here the model is described +by a single real iPEPS tensor and a relative rotation along the :math:`S_y` axis +for interactions with its neighbors. The rotation is set by a spiral vector +which is supplied later in this example. This reduces the computational effort +required for the optimization as only one tensor and not multiple ones have to be +optimized. + +As discussed in the following section, we use the triangular-CTMRG method for +this example, therefore we use the provided expectation class for this case +(:obj:`~varipeps.expectation.triangular_two_sites.Triangular_Two_Sites_Expectation_Value`). + +Initial unit cell construction +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +.. code-block:: python + + # Unit cell structure + structure = [[0]] + +Here we define the unit cell structure which is used to simulate our model. As +noted in the section above, due to the spiral ansatz we only need a single iPEPS +site. + +.. code-block:: python + + # Create random initialization for the iPEPS unit cell + unitcell = varipeps.peps.PEPS_Unit_Cell.random( + structure, # Unit cell structure + p, # Physical dimension + chiB, # iPEPS bond dimension + startChi, # Start value for enviroment bond dimension + float, # Data type for the tensors: `float` (real) or `complex` tensors + max_chi=maxChi, # Maximal enviroment bond dimension + peps_type=varipeps.peps.PEPS_Type.TRIANGULAR, # Select triangular PEPS + ) + +Using the unit cell structure and the model parameter defined above, we can +generate an initial unit cell. Here we initialize the iPEPS tensors with random +numbers. Other ways to initialize the tensors are provided, for example loading results +from a simple update calculation. + +As we simulate a triangular lattice, we use the triangular-CTMRG method +described in `Phys. Rev. B 113, 045117 (2026) +`_. This is selected at the time of creation +of the unit cell by the ``peps_type`` parameter. + +Run the optimization +^^^^^^^^^^^^^^^^^^^^ + +.. code-block:: python + + # Run optimization + result = varipeps.optimization.optimize_unitcell_fixed_spiral_vector( + unitcell, + jnp.array((2 / 3, 2 / 3), dtype=jnp.float64), # Spiral vector + exp_func, + autosave_filename=f"data/autosave_triangular_chiB_{chiB:d}_chiMax_{maxChi:d}.hdf5", + ) + +This function call executes the main function of the library, the variational +energy optimization to obtain a good ground state candidate. We use one of the +wrapper around the main optimization function which is predefined for the case +of a spiral PEPS ansatz with a fixed value for the spiral vector. There are +other variants for example for the variational optimization of the full spiral +vector or for the optimization of just the :math:`x`- or :math:`y`-component. +The other arguments are the function for calculating the energy expectation +value, and a file path for autosaving the optimization process, enabling the +restoration of interrupted simulations. + +Evaluate the results +^^^^^^^^^^^^^^^^^^^^ + +In this section we show some exemplary evaluation of the result of the optimization. + +.. code-block:: python + + # Calculate magnetic expectation values + Mag_Gates = [Sx, Sy, Sz] + + + def calc_magnetic(unitcell): + mag_result = [] + for ti, t in enumerate(unitcell.get_unique_tensors()): + r = varipeps.expectation.one_site.calc_one_site_multi_gates( + t.tensor, t, Mag_Gates + ) + mag_result += r + return mag_result + + + magnetic_exp_values = calc_magnetic(result.unitcell) + +We assume for our example that we are interested in the single-site spin +expectation values. These could be used to analyse the :math:`z`-magnetization +or the staggered magnetization of our model at/near the ground state. + +.. code-block:: python + + # Define some auxiliary data which should be stored along the final iPEPS unit cell + auxiliary_data = { + "best_energy": result.fun, + "best_run": result.best_run, + "magnetic_exp_values": magnetic_exp_values, + } + for k in sorted(result.max_trunc_error_list.keys()): + auxiliary_data[f"max_trunc_error_list_{k:d}"] = result.max_trunc_error_list[k] + auxiliary_data[f"step_energies_{k:d}"] = result.step_energies[k] + auxiliary_data[f"step_chi_{k:d}"] = result.step_chi[k] + auxiliary_data[f"step_conv_{k:d}"] = result.step_conv[k] + auxiliary_data[f"step_runtime_{k:d}"] = result.step_runtime[k] + + # save full iPEPS state + result.unitcell.save_to_file( + f"data/heisenberg_triangular_J_{J:d}_chiB_{chiB:d}_chiMax_{maxChi:d}.hdf5", + auxiliary_data=auxiliary_data, + ) + +Finally, we want to save the unit cell with the optimized tensors to a file for +further analysis. The library allows to store the data directly into a +HDF5 file along with user-supplied auxiliary data. Here, for example, we not only +want to store the plain tensors but also the calculated energy, meta information +from the optimization run (e.g. energy per step or the runtime per step) and the +calculated magnetic expectation values. At a later examination of the results, +these data can be easily loaded along with the tensors of the tensor network. diff --git a/data/docs/source/examples/index.rst b/data/docs/source/examples/index.rst new file mode 100644 index 0000000000000000000000000000000000000000..c8273adb56b7e117db022e2235ec0ffc9bd8b4ca --- /dev/null +++ b/data/docs/source/examples/index.rst @@ -0,0 +1,13 @@ +.. _examples: + + +Overview +======== + +We provide several examples in the `examples/ folder of the variPEPS Git +repository `_ +that demonstrate how to use the code for variational energy optimization in +typical 2D many-body problems. + +In the documentation we include a commented version of the examples with a +detailed description of the model and the consideration how to call the library. diff --git a/data/docs/source/general.rst b/data/docs/source/general.rst new file mode 100644 index 0000000000000000000000000000000000000000..b281ec74aab16c52a856183c263e9463ff394b0d --- /dev/null +++ b/data/docs/source/general.rst @@ -0,0 +1,77 @@ +.. _general: + + +Introduction +============ + +variPEPS is a Python tensor network library developed for variational ground +state simulations in two spatial dimensions applying gradient optimization using +automatic differentation. + +For a detailed report on the method, please see `our open-access publication on +SciPost (doi:10.21468/SciPostPhysLectNotes.86) +`_. + +Installation using pip +====================== + +The current version of the variPEPS Python package is available on `PyPI +`_. It can be easily installed using the +Python package manager pip: + +.. code-block:: console + + $ python3 -m pip install variPEPS + +Core Features +============= + +* Calculation of expectation values, structure factors, overlaps and correlation + lengths of infinite PEPS states. +* Variational optimization for ground state search of Hamiltonian models using + automatic differentiation. +* Predefined mappings of other lattices (kagome, maple-leaf, ...) to square and + triangular PEPS structure. +* Support for spiral-PEPS method (`Phys. Rev. Lett. 133, 176502 (2024) + `_). +* Reference implementation of the split-CTMRG (`Phys. Rev. B 111, 235116 (2025) + `_) and triangular-CTMRG + (`Phys. Rev. B 113, 045117 (2026) `_) + variants. +* Direct support of just-in-time compilation (JIT) and GPU devices thanks to the + :obj:`jax` framework. + +Usage +===== + +The :obj:`varipeps` module is organized in several submodules corresponding to +the different features. For a variational optimization the most important parts +are (a full overview can be found in the :ref:`api`): + +* :obj:`varipeps.peps`: To define iPEPS unit cell and the tensors on each site, + the library provides in this submodule the abstractions to define such a unit + cell. +* :obj:`varipeps.expectation`: In this submodule the helper functions to define + and calculate common expecation functions on the iPEPS unit + cell. Particularly, the function can be used to define the Hamiltonian terms + of the model of interest. +* :obj:`varipeps.mapping`: If not only interactions on the square lattice are of + interest but also models on other 2d lattices, in this submodule one can find + mappings of other lattices. Also the files there can be a good starting point + to implement even more lattices. +* :obj:`varipeps.optimization`: The submodule providing the optimization + algorithm and interface of the library. In almost all cases, one will interact + with this part by the main function + :obj:`varipeps.optimization.optimize_peps_network` or the convience wrapper around t. + +All these different modules can be seen in action in the :ref:`examples` +section of the documentation where exemplary code is discussed in detail. + +Citation +======== + +We are happy if you want to use the framework for your research. To cite our +work we provide a list of our preferred references on the `GitHub page of the +project +`_. Please +check there for a current list. diff --git a/data/docs/source/images/CTMRG_Absorption_D_C3.pdf b/data/docs/source/images/CTMRG_Absorption_D_C3.pdf new file mode 100644 index 0000000000000000000000000000000000000000..bf1c6f8f3c5bcfa2b0e3a35dc31862cf72da4a8f Binary files /dev/null and b/data/docs/source/images/CTMRG_Absorption_D_C3.pdf differ diff --git a/data/docs/source/images/CTMRG_Absorption_D_C3.svg b/data/docs/source/images/CTMRG_Absorption_D_C3.svg new file mode 100644 index 0000000000000000000000000000000000000000..abcf3e229ab1854a0ca44f7536395bdeaf8132fc --- /dev/null +++ b/data/docs/source/images/CTMRG_Absorption_D_C3.svg @@ -0,0 +1,535 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/data/docs/source/images/CTMRG_Absorption_D_C3.tex b/data/docs/source/images/CTMRG_Absorption_D_C3.tex new file mode 100644 index 0000000000000000000000000000000000000000..a5eda7b13dbbb6cfa37a13db8eeb15e1bc3cf3f2 --- /dev/null +++ b/data/docs/source/images/CTMRG_Absorption_D_C3.tex @@ -0,0 +1,78 @@ +\documentclass[tikz]{standalone} + +\usepackage{amsfonts} +\usepackage{amsmath} +\usepackage{braket} + +\usepackage{tikz} +\usetikzlibrary{calc, decorations, positioning} + +% load TikZ grafic definitions +%\input{gfx_TikZ} + +% main document +\begin{document} + + \begin{tikzpicture}[] + + % contant definitions + \def\tensorSize{0.2} + + % tensor network contraction + \begin{scope} + + % iPEPS network coordinates + \coordinate (PN) at (+0.0, +0.5); + \coordinate (PC) at (+0.0, -0.5); + + % CTMRG network coordinates + \coordinate (C1) at (-0.5, +1.5); + \coordinate (T1) at (+1.5, +1.5); + \coordinate (C2) at (+3.5, +1.5); + \coordinate (T2) at (+2.0, +0.0); + \coordinate (C3) at (+0.5, -1.5); + \coordinate (T3) at (-1.5, -1.5); + \coordinate (C4) at (-3.5, -1.5); + \coordinate (T4) at (-2.0, -0.0); + + % projector P_{UL} + \begin{scope}[shift = {(-1.50, -0.50)}] + \coordinate (PLL) at (+0.00, +0.00); + \coordinate (PLU) at (+2.00, +1.00); + \coordinate (PLM) at (+1.00, +0.00); + \coordinate (PLD) at (+0.00, -1.00); + \node[] at (+0.00, +1.00) {$P_\text{D(L)}^{[x, y]}$}; + \end{scope} + + % tensor labels + \node[right = 0.25] at (T2) {$T_{2}^{[x, y]}$}; + \node[below = 0.25] at (C3) {$C_{3}^{[x, y]}$}; + + % external links + \draw[ultra thick] (PLL) to ($(PLL) + (-1.50, +0.00)$) node at ($(PLL) + (-2.00, +0.00)$) {$-1$}; + \draw[ultra thick] (T2) to ($(T2) + (+0.75, +0.75)$) node at ($(T2) + (+1.00, +1.00)$) {$-2$}; + + % projector + \draw[thick, fill = gray!25] (PLL) to (PLU) to (PLD) -- cycle; + + % internal links + \draw[ultra thick] (C3) -- (PLD) node[above] at ($(C3)!0.5!(PLD)$) {$2$}; + \draw[ultra thick] (C3) -- (T2) node [midway, right = 0.25] {$1$}; + \draw[thick] (T2) to [out = 180, in = 0] (PLU) node[above] at ($(T2)!0.5!(PLU)$) {$4$}; + \draw[thick] (T2) to [out = 180, in = 0] (PLM) node[below] at ($(T2)!0.5!(PLM)$) {$3$}; + + % CTMRG tensors + \foreach \tensor in {C3, T2} { + \draw[thick,black,fill = gray] (\tensor) circle (\tensorSize); + } + + \end{scope} + + \end{tikzpicture} + +\end{document} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: diff --git a/data/docs/source/images/CTMRG_Absorption_D_C4.pdf b/data/docs/source/images/CTMRG_Absorption_D_C4.pdf new file mode 100644 index 0000000000000000000000000000000000000000..9ecae9532083c37b94d04d822bcd104b4e8c7f13 Binary files /dev/null and b/data/docs/source/images/CTMRG_Absorption_D_C4.pdf differ diff --git a/data/docs/source/images/CTMRG_Absorption_D_C4.svg b/data/docs/source/images/CTMRG_Absorption_D_C4.svg new file mode 100644 index 0000000000000000000000000000000000000000..1533270c7ce0be89930d13e0060e1c7818810250 --- /dev/null +++ b/data/docs/source/images/CTMRG_Absorption_D_C4.svg @@ -0,0 +1,545 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/data/docs/source/images/CTMRG_Absorption_D_C4.tex b/data/docs/source/images/CTMRG_Absorption_D_C4.tex new file mode 100644 index 0000000000000000000000000000000000000000..7fed3c4a240ad9de947e4069767b5744a2a4e703 --- /dev/null +++ b/data/docs/source/images/CTMRG_Absorption_D_C4.tex @@ -0,0 +1,77 @@ +\documentclass[tikz]{standalone} + +\usepackage{amsfonts} +\usepackage{amsmath} +\usepackage{braket} + +\usepackage{tikz} +\usetikzlibrary{calc, decorations, positioning} + +% load TikZ grafic definitions +%\input{gfx_TikZ} + +% main document +\begin{document} + + \begin{tikzpicture}[] + + % contant definitions + \def\tensorSize{0.2} + + % tensor network contraction + \begin{scope} + + % iPEPS network coordinates + \coordinate (PN) at (+0.0, +0.5); + \coordinate (PC) at (+0.0, -0.5); + + % CTMRG network coordinates + \coordinate (C1) at (-0.5, +1.5); + \coordinate (T1) at (+1.5, +1.5); + \coordinate (C2) at (+3.5, +1.5); + \coordinate (T2) at (+2.0, +0.0); + \coordinate (C3) at (+0.5, -1.5); + \coordinate (T3) at (-1.5, -1.5); + \coordinate (C4) at (-3.5, -1.5); + \coordinate (T4) at (-2.0, -0.0); + + % projector P_{UR} + \begin{scope}[shift = {(+0.50, -0.50)}] + \coordinate (PRU) at (+0.00, +1.00); + \coordinate (PRM) at (-1.00, -0.00); + \coordinate (PRD) at (-2.00, -1.00); + \coordinate (PRR) at (+0.00, +0.00); + \node[] at (-0.00, -1.00) {$P_\text{D(R)}^{[x, y - 1]}$}; + \end{scope} + + % tensor labels + \node[below = 0.25] at (C4) {$C_{4}^{[x, y]}$}; + \node[left = 0.25] at (T4) {$T_{4}^{[x, y]}$}; + + % external links + \draw[ultra thick] (PRR) to ($(PRR) + (+1.50, +0.00)$) node at ($(PRR) + (+2.00, +0.00)$) {$-1$}; + \draw[ultra thick] (T4) to ($(T4) + (+0.75, +0.75)$) node at ($(T4) + (+1.00, +1.00)$) {$-2$}; + + % projector + \draw[thick, fill = gray!25] (PRR) to (PRU) to (PRD) -- cycle; + + % internal links + \draw[ultra thick] (PRD) -- (C4) node[above] at ($(C4)!0.5!(PRD)$) {$2$}; + \draw[ultra thick] (C4) -- (T4) node [midway, left = 0.25] {$1$}; + \draw[thick] (PRU) to [out = 180, in = 0] (T4) node[above] at ($(PRU)!0.5!(T4)$) {$4$}; + \draw[thick] (PRM) to [out = 180, in = 0] (T4) node[below] at ($(PRM)!0.5!(T4)$) {$3$}; + + % CTMRG tensors + \foreach \tensor in {T4, C4} { + \draw[thick,black,fill = gray] (\tensor) circle (\tensorSize); + } + + \end{scope} + + \end{tikzpicture} + +\end{document} +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: diff --git a/data/docs/source/images/CTMRG_Absorption_D_T3.pdf b/data/docs/source/images/CTMRG_Absorption_D_T3.pdf new file mode 100644 index 0000000000000000000000000000000000000000..13b13b0696010415ae90d35273c2b0200d3bea20 Binary files /dev/null and b/data/docs/source/images/CTMRG_Absorption_D_T3.pdf differ diff --git a/data/docs/source/images/CTMRG_Absorption_D_T3.svg b/data/docs/source/images/CTMRG_Absorption_D_T3.svg new file mode 100644 index 0000000000000000000000000000000000000000..f38bd745bc58f09de88d5f99904ea5c2fa11463b --- /dev/null +++ b/data/docs/source/images/CTMRG_Absorption_D_T3.svg @@ -0,0 +1,783 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/data/docs/source/images/CTMRG_Absorption_D_T3.tex b/data/docs/source/images/CTMRG_Absorption_D_T3.tex new file mode 100644 index 0000000000000000000000000000000000000000..b19430fdeb468c4da48dffd33f932eb147b28354 --- /dev/null +++ b/data/docs/source/images/CTMRG_Absorption_D_T3.tex @@ -0,0 +1,99 @@ +\documentclass[tikz]{standalone} + +\usepackage{amsfonts} +\usepackage{amsmath} +\usepackage{braket} + +\usepackage{tikz} +\usetikzlibrary{calc, decorations, positioning} + +% load TikZ grafic definitions +%\input{gfx_TikZ} + +% main document +\begin{document} + + \begin{tikzpicture}[] + + % contant definitions + \def\tensorSize{0.2} + + % tensor network contraction + \begin{scope} + + % iPEPS network coordinates + \coordinate (PN) at (+0.0, +0.5); + \coordinate (PC) at (+0.0, -0.5); + + % CTMRG network coordinates + \coordinate (C1) at (-0.5, +1.5); + \coordinate (T1) at (+1.5, +1.5); + \coordinate (C2) at (+3.5, +1.5); + \coordinate (T2) at (+2.0, +0.0); + \coordinate (C3) at (+0.5, -1.5); + \coordinate (T3) at (-1.5, -1.5); + \coordinate (C4) at (-3.5, -1.5); + \coordinate (T4) at (-2.0, -0.0); + + % projector P_{UL} + \begin{scope}[shift = {(-3.50, -0.50)}] + \coordinate (PLL) at (+0.00, +0.00); + \coordinate (PLU) at (+2.00, +1.00); + \coordinate (PLM) at (+1.00, +0.00); + \coordinate (PLD) at (+0.00, -1.00); + \node[] at (+0.00, +1.00) {$P_\text{D(L)}^{[x, y - 1]}$}; + \end{scope} + + % projector P_{UR} + \begin{scope}[shift = {(+2.50, -0.50)}] + \coordinate (PRU) at (+0.00, +1.00); + \coordinate (PRM) at (-1.00, -0.00); + \coordinate (PRD) at (-2.00, -1.00); + \coordinate (PRR) at (+0.00, +0.00); + \node[] at (-0.00, -1.00) {$P_\text{D(R)}^{[x, y]}$}; + \end{scope} + + % tensor labels + \node at ($(T3) + (-0.75, -0.75)$) {$T_{3}^{[x, y]}$}; + + % external links + \draw[thick] (PN) to ($(PN) + (+1.50, +1.50)$) node at ($(PN) + (+2.00, +2.00)$) {$-4$}; + \draw[thick] (PC) to ($(PC) + (+1.50, +1.50)$) node at ($(PC) + (+2.00, +2.00)$) {$-3$}; + \draw[ultra thick] (PLL) to ($(PLL) + (-1.50, -0.00)$) node at ($(PLL) + (-2.00, -0.00)$) {$-1$}; + \draw[ultra thick] (PRR) to ($(PRR) + (+1.50, +0.00)$) node at ($(PRR) + (+2.00, +0.00)$) {$-2$}; + + % projectors + \draw[thick, fill = gray!25] (PLL) to (PLU) to (PLD) -- cycle; + \draw[thick, fill = gray!25] (PRR) to (PRU) to (PRD) -- cycle; + + % internal links + \draw[ultra thick] (T3) -- (PLD) node[below] at ($(T3)!0.5!(PLD)$) {$1$}; + \draw[ultra thick] (T3) -- (PRD) node[below] at ($(T3)!0.5!(PRD)$) {$7$}; + \draw[thick] (PN) to [out = 180, in = 0] (PLU) node[below] at ($(PN)!0.7!(PLU)$) {$3$}; + \draw[thick] (PRU) to [out = 180, in = 0] (PN) node[below] at ($(PRU)!0.3!(PN)$) {$8$}; + \draw[thick] (PC) to [out = 180, in = 0] (PLM) node[below] at ($(PC)!0.7!(PLM)$) {$5$}; + \draw[thick] (PRM) to [out = 180, in = 0] (PC) node[below] at ($(PRM)!0.5!(PC)$) {$9$}; + \draw[thick] (T3) to [out = 45, in = 225] (PC) node[right = 0.1] at ($(T3)!0.3!(PC)$) {$4$}; + \draw[thick] (T3) to [out = 45, in = 225] (PN) node[left = 0.1] at ($(T3)!0.3!(PN)$) {$2$}; + \draw[thick] (PN) -- (PC) node [midway, right] {$6$}; + + % CTMRG tensors + \foreach \tensor in {T3} { + \draw[thick,black,fill = gray] (\tensor) circle (\tensorSize); + } + + % iPEPS tensors + \foreach \tensor in {PN, PC} { + \draw[thick,black,fill = blue] (\tensor) circle (\tensorSize); + } + + \end{scope} + + \end{tikzpicture} + +\end{document} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: diff --git a/data/docs/source/images/CTMRG_Absorption_L_C1.pdf b/data/docs/source/images/CTMRG_Absorption_L_C1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..627224ed6ada6aa28821da4e724189727695ca24 Binary files /dev/null and b/data/docs/source/images/CTMRG_Absorption_L_C1.pdf differ diff --git a/data/docs/source/images/CTMRG_Absorption_L_C1.svg b/data/docs/source/images/CTMRG_Absorption_L_C1.svg new file mode 100644 index 0000000000000000000000000000000000000000..7cadf53be36ab68413d6caabb09602cacfd6f308 --- /dev/null +++ b/data/docs/source/images/CTMRG_Absorption_L_C1.svg @@ -0,0 +1,560 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/data/docs/source/images/CTMRG_Absorption_L_C1.tex b/data/docs/source/images/CTMRG_Absorption_L_C1.tex new file mode 100644 index 0000000000000000000000000000000000000000..60a58e199ac09e8458590779c876ce0930598735 --- /dev/null +++ b/data/docs/source/images/CTMRG_Absorption_L_C1.tex @@ -0,0 +1,76 @@ +\documentclass[tikz]{standalone} + +\usepackage{amsfonts} +\usepackage{amsmath} +\usepackage{braket} + +\usepackage{tikz} +\usetikzlibrary{calc, decorations, positioning} + +% load TikZ grafic definitions +%\input{gfx_TikZ} + +% main document +\begin{document} + + \begin{tikzpicture}[] + % contant definitions + \def\tensorSize{0.2} + + % tensor network contraction + \begin{scope} + + % iPEPS network coordinates + \coordinate (PN) at (+0.0, +0.5); + \coordinate (PC) at (+0.0, -0.5); + + % CTMRG network coordinates + \coordinate (C1) at (-0.5, +1.5); + \coordinate (T1) at (+1.5, +1.5); + \coordinate (C2) at (+3.5, +1.5); + \coordinate (T2) at (+2.0, +0.0); + \coordinate (C3) at (+0.5, -1.5); + \coordinate (T3) at (-1.5, -1.5); + \coordinate (C4) at (-3.5, -1.5); + \coordinate (T4) at (-2.0, -0.0); + + % projector P_{LD} + \begin{scope}[shift = {(-0.50, -0.00)}] + \coordinate (PDL) at (-1.00, +0.50); + \coordinate (PDM) at (+0.50, +0.50); + \coordinate (PDR) at (+1.50, +0.50); + \coordinate (PDD) at (-0.50, +0.00); + \node[] at (-1.50, -0.00) {$P_\text{L(D)}^{[x - 1, y]}$}; + \end{scope} + + % tensor labels + \node[above = 0.25] at (C1) {$C_{1}^{[x, y]}$}; + \node[above = 0.25] at (T1) {$T_{1}^{[x, y]}$}; + + % external links + \draw[ultra thick] (PDD) to ($(PDD) + (-0.75, -0.75)$) node at ($(PDD) + (-1.00, -1.00)$) {$-1$}; + \draw[ultra thick] (T1) to ($(T1) + (+1.50, +0.00)$) node at ($(T1) + (+2.00, +0.00)$) {$-2$}; + + % projector + \draw[thick, fill = gray!25] (PDL) to (PDR) to (PDD) -- cycle; + + % internal links + \draw[ultra thick] (C1) -- (PDL) node[left = 0.25] at ($(C1)!0.5!(PDL)$) {$2$}; + \draw[ultra thick] (C1) -- (T1) node [midway, above] {$1$}; + \draw[thick] (T1) to [out = 225, in = 45] (PDM) node[left = 0.25] at ($(T1)!0.5!(PDM)$) {$3$}; + \draw[thick] (T1) to [out = 225, in = 45] (PDR) node[right] at ($(T1)!0.5!(PDR)$) {$4$}; + + % CTMRG tensors + \foreach \tensor in {C1, T1} { + \draw[thick,black,fill = gray] (\tensor) circle (\tensorSize); + } + + \end{scope} + + \end{tikzpicture} + +\end{document} +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: diff --git a/data/docs/source/images/CTMRG_Absorption_L_C4.pdf b/data/docs/source/images/CTMRG_Absorption_L_C4.pdf new file mode 100644 index 0000000000000000000000000000000000000000..ae16711ef7180aebe84a7d4b3402bfd1e7ae337d Binary files /dev/null and b/data/docs/source/images/CTMRG_Absorption_L_C4.pdf differ diff --git a/data/docs/source/images/CTMRG_Absorption_L_C4.svg b/data/docs/source/images/CTMRG_Absorption_L_C4.svg new file mode 100644 index 0000000000000000000000000000000000000000..b16e9a3e52901b0f62092943f29e5a8d1043a223 --- /dev/null +++ b/data/docs/source/images/CTMRG_Absorption_L_C4.svg @@ -0,0 +1,535 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/data/docs/source/images/CTMRG_Absorption_L_C4.tex b/data/docs/source/images/CTMRG_Absorption_L_C4.tex new file mode 100644 index 0000000000000000000000000000000000000000..16783f98ee4fdb96458535966aab10d9ea8e5ee3 --- /dev/null +++ b/data/docs/source/images/CTMRG_Absorption_L_C4.tex @@ -0,0 +1,77 @@ +\documentclass[tikz]{standalone} + +\usepackage{amsfonts} +\usepackage{amsmath} +\usepackage{braket} + +\usepackage{tikz} +\usetikzlibrary{calc, decorations, positioning} + +% load TikZ grafic definitions +%\input{gfx_TikZ} + +% main document +\begin{document} + + \begin{tikzpicture}[] + + % contant definitions + \def\ballSize{0.2} + + % tensor network contraction + \begin{scope} + + % iPEPS network coordinates + \coordinate (PN) at (+0.0, +0.5); + \coordinate (PC) at (+0.0, -0.5); + + % CTMRG network coordinates + \coordinate (C1) at (-0.5, +1.5); + \coordinate (T1) at (+1.5, +1.5); + \coordinate (C2) at (+3.5, +1.5); + \coordinate (T2) at (+2.0, +0.0); + \coordinate (C3) at (+0.5, -1.5); + \coordinate (T3) at (-1.5, -1.5); + \coordinate (C4) at (-3.5, -1.5); + \coordinate (T4) at (-2.0, -0.0); + + % projector P_{LU} + \begin{scope}[shift = {(-1.00, +0.00)}] + \coordinate (PUL) at (-1.50, -0.50); + \coordinate (PUM) at (+0.00, -0.50); + \coordinate (PUR) at (+1.00, -0.50); + \coordinate (PUU) at (+0.50, +0.00); + \node[] at (-1.50, -0.00) {$P_\text{L(U)}^{[x, y]}$}; + \end{scope} + + % tensor labels + \node[below = 0.25] at (C4) {$C_{4}^{[x,y]}$}; + \node[below = 0.25] at (T3) {$T_{3}^{[x,y]}$}; + + % external links + \draw[ultra thick] (PUU) to ($(PUU) + (+0.75, +0.75)$) node at ($(PUU) + (+1.00, +1.00)$) {$-2$}; + \draw[ultra thick] (T3) to ($(T3) + (+1.50, +0.00)$) node at ($(T3) + (+2.00, +0.00)$) {$-1$}; + + % projector + \draw[thick, fill = gray!25] (PUL) to (PUR) to (PUU) -- cycle; + + % internal links + \draw[ultra thick] (C4) -- (PUL) node[left = 0.25] at ($(C4)!0.5!(PUL)$) {$2$}; + \draw[ultra thick] (C4) -- (T3) node [midway, below] {$1$}; + \draw[thick] (T3) to [out = 45, in = 225] (PUM) node[left = 0.25] at ($(T3)!0.5!(PUM)$) {$3$}; + \draw[thick] (T3) to [out = 45, in = 225] (PUR) node[right] at ($(T3)!0.5!(PUR)$) {$4$}; + + % CTMRG tensors + \foreach \tensor in {T3, C4} { + \draw[thick,black,fill = gray] (\tensor) circle (\ballSize); + } + + \end{scope} + + \end{tikzpicture} + +\end{document} +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: diff --git a/data/docs/source/images/CTMRG_Absorption_L_T4.pdf b/data/docs/source/images/CTMRG_Absorption_L_T4.pdf new file mode 100644 index 0000000000000000000000000000000000000000..a42b0679529984e4b20edf8701dbe6e499303991 Binary files /dev/null and b/data/docs/source/images/CTMRG_Absorption_L_T4.pdf differ diff --git a/data/docs/source/images/CTMRG_Absorption_L_T4.svg b/data/docs/source/images/CTMRG_Absorption_L_T4.svg new file mode 100644 index 0000000000000000000000000000000000000000..0187aea397a02024531fc7e1bdfc9f1b4eea8a9d --- /dev/null +++ b/data/docs/source/images/CTMRG_Absorption_L_T4.svg @@ -0,0 +1,815 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/data/docs/source/images/CTMRG_Absorption_L_T4.tex b/data/docs/source/images/CTMRG_Absorption_L_T4.tex new file mode 100644 index 0000000000000000000000000000000000000000..586c44caeba0ebaefafe7b7718492181419738eb --- /dev/null +++ b/data/docs/source/images/CTMRG_Absorption_L_T4.tex @@ -0,0 +1,98 @@ +\documentclass[tikz]{standalone} + +\usepackage{amsfonts} +\usepackage{amsmath} +\usepackage{braket} + +\usepackage{tikz} +\usetikzlibrary{calc, decorations, positioning} + +% load TikZ grafic definitions +%\input{gfx_TikZ} + +% main document +\begin{document} + + \begin{tikzpicture}[] + + % contant definitions + \def\tensorSize{0.2} + + % tensor network contraction + \begin{scope} + + % iPEPS network coordinates + \coordinate (PN) at (+0.0, +0.5); + \coordinate (PC) at (+0.0, -0.5); + + % CTMRG network coordinates + \coordinate (C1) at (-0.5, +1.5); + \coordinate (T1) at (+1.5, +1.5); + \coordinate (C2) at (+3.5, +1.5); + \coordinate (T2) at (+2.0, +0.0); + \coordinate (C3) at (+0.5, -1.5); + \coordinate (T3) at (-1.5, -1.5); + \coordinate (C4) at (-3.5, -1.5); + \coordinate (T4) at (-2.0, -0.0); + + % projector P_{LU} + \begin{scope}[shift = {(+1.00, +2.00)}] + \coordinate (PUL) at (-1.50, -0.50); + \coordinate (PUM) at (+0.00, -0.50); + \coordinate (PUR) at (+1.00, -0.50); + \coordinate (PUU) at (+0.50, +0.00); + \node[] at (-1.50, -0.00) {$P_\text{L(U)}^{[x - 1, y]}$}; + \end{scope} + + % projector P_{LD} + \begin{scope}[shift = {(-2.50, -2.00)}] + \coordinate (PDL) at (-1.00, +0.50); + \coordinate (PDM) at (+0.50, +0.50); + \coordinate (PDR) at (+1.50, +0.50); + \coordinate (PDD) at (-0.50, +0.00); + \node[] at (-1.50, -0.00) {$P_\text{L(D)}^{[x, y]}$}; + \end{scope} + + % tensor labels + \node at (-3.0, +0) {$T_4^{[x, y]}$}; + + % external links + \draw[thick] (PN) to ($(PN) + (+2.00, +0.00)$) node at ($(PN) + (+2.50, +0.00)$) {$-3$}; + \draw[thick] (PC) to ($(PC) + (+1.00, +0.00)$) node at ($(PC) + (+1.50, +0.00)$) {$-2$}; + \draw[ultra thick] (PDD) to ($(PDD) + (-1.00, -1.00)$) node at ($(PDD) + (-1.25, -1.25)$) {$-1$}; + \draw[ultra thick] (PUU) to ($(PUU) + (+1.00, +1.00)$) node at ($(PUU) + (+1.25, +1.25)$) {$-4$}; + + % projectors + \draw[thick, fill = gray!25] (PUL) to (PUR) to (PUU) -- cycle; + \draw[thick, fill = gray!25] (PDL) to (PDR) to (PDD) -- cycle; + + % internal links + \draw[ultra thick] (T4) -- (PDL) node[left = 0.25] at ($(T4)!0.5!(PDL)$) {$7$}; + \draw[ultra thick] (T4) -- (PUL) node[left = 0.25] at ($(T4)!0.5!(PUL)$) {$1$}; + \draw[thick] (PN) to [out = 225, in = 45] (PDM) node[left = 0.25] at ($(PN)!0.7!(PDM)$) {$8$}; + \draw[thick] (PUM) to [out = 225, in = 45] (PN) node[left = 0.25] at ($(PUM)!0.3!(PN)$) {$2$}; + \draw[thick] (PC) to [out = 225, in = 45] (PDR) node[right] at ($(PC)!0.7!(PDR)$) {$9$}; + \draw[thick] (PUR) to [out = 225, in = 45] (PC) node[right] at ($(PUR)!0.3!(PC)$) {$5$}; + \draw[thick] (T4) to [out = 0, in = 180] (PC) node[below] at ($(T4)!0.3!(PC)$) {$4$}; + \draw[thick] (T4) to [out = 0, in = 180] (PN) node[above] at ($(T4)!0.7!(PN)$) {$3$}; + \draw[thick] (PN) -- (PC) node [midway, right] {$6$}; + + % CTMRG tensors + \foreach \tensor in {T4} { + \draw[thick,black,fill = gray] (\tensor) circle (\tensorSize); + } + + % iPEPS tensors + \foreach \tensor in {PN, PC} { + \draw[thick,black,fill = blue] (\tensor) circle (\tensorSize); + } + + \end{scope} + + \end{tikzpicture} + +\end{document} +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: diff --git a/data/docs/source/images/CTMRG_Absorption_R_C2.pdf b/data/docs/source/images/CTMRG_Absorption_R_C2.pdf new file mode 100644 index 0000000000000000000000000000000000000000..9f333c4922e24c2d46d8f3c31c94c69ca3cb199d Binary files /dev/null and b/data/docs/source/images/CTMRG_Absorption_R_C2.pdf differ diff --git a/data/docs/source/images/CTMRG_Absorption_R_C2.svg b/data/docs/source/images/CTMRG_Absorption_R_C2.svg new file mode 100644 index 0000000000000000000000000000000000000000..fbeaeb00dd27af09ab3bac2cda3a10fb04515719 --- /dev/null +++ b/data/docs/source/images/CTMRG_Absorption_R_C2.svg @@ -0,0 +1,592 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/data/docs/source/images/CTMRG_Absorption_R_C2.tex b/data/docs/source/images/CTMRG_Absorption_R_C2.tex new file mode 100644 index 0000000000000000000000000000000000000000..99d983cbc7037afd10af6138463abcc1ea5653a6 --- /dev/null +++ b/data/docs/source/images/CTMRG_Absorption_R_C2.tex @@ -0,0 +1,78 @@ +\documentclass[tikz]{standalone} + +\usepackage{amsfonts} +\usepackage{amsmath} +\usepackage{braket} + +\usepackage{tikz} +\usetikzlibrary{calc, decorations, positioning} + +% load TikZ grafic definitions +%\input{gfx_TikZ} + +% main document +\begin{document} + + \begin{tikzpicture}[] + + % contant definitions + \def\tensorSize{0.2} + + % tensor network contraction + \begin{scope} + + % iPEPS network coordinates + \coordinate (PN) at (+0.0, +0.5); + \coordinate (PC) at (+0.0, -0.5); + + % CTMRG network coordinates + \coordinate (C1) at (-0.5, +1.5); + \coordinate (T1) at (+1.5, +1.5); + \coordinate (C2) at (+3.5, +1.5); + \coordinate (T2) at (+2.0, +0.0); + \coordinate (C3) at (+0.5, -1.5); + \coordinate (T3) at (-1.5, -1.5); + \coordinate (C4) at (-3.5, -1.5); + \coordinate (T4) at (-2.0, -0.0); + + % P_{RD} + % projector P_{RD} + \begin{scope}[shift = {(+1.00, -0.00)}] + \coordinate (PDL) at (-1.00, +0.50); + \coordinate (PDM) at (+0.00, +0.50); + \coordinate (PDR) at (+1.50, +0.50); + \coordinate (PDD) at (-0.50, +0.00); + \node[] at (+1.50, -0.00) {$P_\text{R(D)}^{[x - 1, y]}$}; + \end{scope} + + % tensor labels + \node[above = 0.25] at (C2) {$C_{2}^{[x, y]}$}; + \node[above = 0.25] at (T1) {$T_{1}^{[x, y]}$}; + + % external links + \draw[ultra thick] (PDD) to ($(PDD) + (-0.75, -0.75)$) node at ($(PDD) + (-1.00, -1.00)$) {$-2$}; + \draw[ultra thick] (T1) to ($(T1) + (-1.50, +0.00)$) node at ($(T1) + (-2.00, +0.00)$) {$-1$}; + + % projector + \draw[thick, fill = gray!25] (PDL) to (PDR) to (PDD) -- cycle; + + % internal links + \draw[ultra thick] (C2) -- (PDR) node[right = 0.25] at ($(C2)!0.5!(PDR)$) {$2$}; + \draw[ultra thick] (C2) -- (T1) node [midway, above] {$1$}; + \draw[thick] (T1) to [out = 225, in = 45] (PDM) node[right] at ($(T1)!0.5!(PDM)$) {$3$}; + \draw[thick] (T1) to [out = 225, in = 45] (PDL) node[above left] at ($(T1)!0.5!(PDL)$) {$4$}; + + % CTMRG tensors + \foreach \tensor in {T1, C2} { + \draw[thick,black,fill = gray] (\tensor) circle (\tensorSize); + } + + \end{scope} + + \end{tikzpicture} + +\end{document} +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: diff --git a/data/docs/source/images/CTMRG_Absorption_R_C3.pdf b/data/docs/source/images/CTMRG_Absorption_R_C3.pdf new file mode 100644 index 0000000000000000000000000000000000000000..672a64c7cfbf90c127a1738752645122869ec3b4 Binary files /dev/null and b/data/docs/source/images/CTMRG_Absorption_R_C3.pdf differ diff --git a/data/docs/source/images/CTMRG_Absorption_R_C3.svg b/data/docs/source/images/CTMRG_Absorption_R_C3.svg new file mode 100644 index 0000000000000000000000000000000000000000..314590195f707fae43ac7e3b02eedb96488f3283 --- /dev/null +++ b/data/docs/source/images/CTMRG_Absorption_R_C3.svg @@ -0,0 +1,529 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/data/docs/source/images/CTMRG_Absorption_R_C3.tex b/data/docs/source/images/CTMRG_Absorption_R_C3.tex new file mode 100644 index 0000000000000000000000000000000000000000..847a3d432b4906f1112cf830bc5611e37e179897 --- /dev/null +++ b/data/docs/source/images/CTMRG_Absorption_R_C3.tex @@ -0,0 +1,77 @@ +\documentclass[tikz]{standalone} + +\usepackage{amsfonts} +\usepackage{amsmath} +\usepackage{braket} + +\usepackage{tikz} +\usetikzlibrary{calc, decorations, positioning} + +% load TikZ grafic definitions +%\input{gfx_TikZ} + +% main document +\begin{document} + + \begin{tikzpicture}[] + + % contant definitions + \def\ballSize{0.2} + + % tensor network contraction + \begin{scope} + + % iPEPS network coordinates + \coordinate (PN) at (+0.0, +0.5); + \coordinate (PC) at (+0.0, -0.5); + + % CTMRG network coordinates + \coordinate (C1) at (-0.5, +1.5); + \coordinate (T1) at (+1.5, +1.5); + \coordinate (C2) at (+3.5, +1.5); + \coordinate (T2) at (+2.0, +0.0); + \coordinate (C3) at (+0.5, -1.5); + \coordinate (T3) at (-1.5, -1.5); + \coordinate (C4) at (-3.5, -1.5); + \coordinate (T4) at (-2.0, -0.0); + + % projector P_{RU} + \begin{scope}[shift = {(+0.50, +0.00)}] + \coordinate (PUL) at (-1.50, -0.50); + \coordinate (PUM) at (-0.50, -0.50); + \coordinate (PUR) at (+1.00, -0.50); + \coordinate (PUU) at (+0.50, +0.00); + \node[] at (+1.50, -0.00) {$P_\text{R(U)}^{[x, y]}$}; + \end{scope} + + % tensor labels + \node[below = 0.25] at (C3) {$C_{3}^{[x,y]}$}; + \node[below = 0.25] at (T3) {$T_{3}^{[x,y]}$}; + + % external links + \draw[ultra thick] (PUU) to ($(PUU) + (+0.75, +0.75)$) node at ($(PUU) + (+1.00, +1.00)$) {$-2$}; + \draw[ultra thick] (T3) to ($(T3) + (-1.50, +0.00)$) node at ($(T3) + (-2.00, +0.00)$) {$-1$}; + + % projector + \draw[thick, fill = gray!25] (PUL) to (PUR) to (PUU) -- cycle; + + % internal links + \draw[ultra thick] (C3) -- (PUR) node[right = 0.25] at ($(C3)!0.5!(PUR)$) {$2$}; + \draw[ultra thick] (C3) -- (T3) node [midway, below] {$1$}; + \draw[thick] (T3) to [out = 45, in = 225] (PUM) node[below right] at ($(T3)!0.5!(PUM)$) {$3$}; + \draw[thick] (T3) to [out = 45, in = 225] (PUL) node[left] at ($(T3)!0.5!(PUL)$) {$4$}; + + % CTMRG tensors + \foreach \tensor in {T3, C3} { + \draw[thick,black,fill = gray] (\tensor) circle (\ballSize); + } + + \end{scope} + + \end{tikzpicture} + +\end{document} +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: diff --git a/data/docs/source/images/CTMRG_Absorption_R_T2.pdf b/data/docs/source/images/CTMRG_Absorption_R_T2.pdf new file mode 100644 index 0000000000000000000000000000000000000000..b266cf243813e95cfe219922f8b5f0bb9ad0c0d0 Binary files /dev/null and b/data/docs/source/images/CTMRG_Absorption_R_T2.pdf differ diff --git a/data/docs/source/images/CTMRG_Absorption_R_T2.svg b/data/docs/source/images/CTMRG_Absorption_R_T2.svg new file mode 100644 index 0000000000000000000000000000000000000000..bdc879fc277b9d63d6c1c90c6d0c8910e3987d60 --- /dev/null +++ b/data/docs/source/images/CTMRG_Absorption_R_T2.svg @@ -0,0 +1,815 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/data/docs/source/images/CTMRG_Absorption_R_T2.tex b/data/docs/source/images/CTMRG_Absorption_R_T2.tex new file mode 100644 index 0000000000000000000000000000000000000000..a7a17bcc23209136eebf54871fd9b025d2a96173 --- /dev/null +++ b/data/docs/source/images/CTMRG_Absorption_R_T2.tex @@ -0,0 +1,98 @@ +\documentclass[tikz]{standalone} + +\usepackage{amsfonts} +\usepackage{amsmath} +\usepackage{braket} + +\usepackage{tikz} +\usetikzlibrary{calc, decorations, positioning} + +% load TikZ grafic definitions +%\input{gfx_TikZ} + +% main document +\begin{document} + + \begin{tikzpicture}[] + + % contant definitions + \def\tensorSize{0.2} + + % tensor network contraction + \begin{scope} + + % iPEPS network coordinates + \coordinate (PN) at (+0.0, +0.5); + \coordinate (PC) at (+0.0, -0.5); + + % CTMRG network coordinates + \coordinate (C1) at (-0.5, +1.5); + \coordinate (T1) at (+1.5, +1.5); + \coordinate (C2) at (+3.5, +1.5); + \coordinate (T2) at (+2.0, +0.0); + \coordinate (C3) at (+0.5, -1.5); + \coordinate (T3) at (-1.5, -1.5); + \coordinate (C4) at (-3.5, -1.5); + \coordinate (T4) at (-2.0, -0.0); + + % projector P_{RU} + \begin{scope}[shift = {(+2.50, +2.00)}] + \coordinate (PUL) at (-1.50, -0.50); + \coordinate (PUM) at (-0.50, -0.50); + \coordinate (PUR) at (+1.00, -0.50); + \coordinate (PUU) at (+0.50, +0.00); + \node[] at (-1.50, -0.00) {$P_\text{R(U)}^{[x - 1, y]}$}; + \end{scope} + + % projector P_{RD} + \begin{scope}[shift = {(-1.00, -2.00)}] + \coordinate (PDL) at (-1.00, +0.50); + \coordinate (PDM) at (+0.00, +0.50); + \coordinate (PDR) at (+1.50, +0.50); + \coordinate (PDD) at (-0.50, +0.00); + \node[] at (-1.50, -0.00) {$P_\text{R(D)}^{[x, y]}$}; + \end{scope} + + % tensor labels + \node at (+3.0, +0) {$T_{2}^{[x, y]}$}; + + % external links + \draw[thick] (PN) to ($(PN) + (-1.00, +0.00)$) node at ($(PN) + (-1.50, +0.00)$) {$-1$}; + \draw[thick] (PC) to ($(PC) + (-2.00, +0.00)$) node at ($(PC) + (-2.50, +0.00)$) {$-2$}; + \draw[ultra thick] (PDD) to ($(PDD) + (-1.00, -1.00)$) node at ($(PDD) + (-1.25, -1.25)$) {$-3$}; + \draw[ultra thick] (PUU) to ($(PUU) + (+1.00, +1.00)$) node at ($(PUU) + (+1.25, +1.25)$) {$-4$}; + + % projectors + \draw[thick, fill = gray!25] (PUL) to (PUR) to (PUU) -- cycle; + \draw[thick, fill = gray!25] (PDL) to (PDR) to (PDD) -- cycle; + + % internal links + \draw[ultra thick] (T2) -- (PDR) node[right = 0.25] at ($(T2)!0.5!(PDR)$) {$7$}; + \draw[ultra thick] (T2) -- (PUR) node[right = 0.25] at ($(T2)!0.5!(PUR)$) {$1$}; + \draw[thick] (PN) to [out = 225, in = 45] (PDL) node[left = 0.25] at ($(PN)!0.7!(PDL)$) {$8$}; + \draw[thick] (PUL) to [out = 225, in = 45] (PN) node[left = 0.25] at ($(PUL)!0.3!(PN)$) {$2$}; + \draw[thick] (PC) to [out = 225, in = 45] (PDM) node[right] at ($(PC)!0.7!(PDM)$) {$9$}; + \draw[thick] (PUM) to [out = 225, in = 45] (PC) node[right] at ($(PUM)!0.3!(PC)$) {$4$}; + \draw[thick] (T2) to [out = 180, in = 0] (PC) node[below] at ($(T2)!0.3!(PC)$) {$5$}; + \draw[thick] (T2) to [out =180, in = 0] (PN) node[above] at ($(T2)!0.7!(PN)$) {$3$}; + \draw[thick] (PN) -- (PC) node [midway, right] {$6$}; + + % CTMRG tensors + \foreach \tensor in {T2} { + \draw[thick,black,fill = gray] (\tensor) circle (\tensorSize); + } + + % iPEPS tensors + \foreach \tensor in {PN, PC} { + \draw[thick,black,fill = blue] (\tensor) circle (\tensorSize); + } + + \end{scope} + + \end{tikzpicture} + +\end{document} +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: diff --git a/data/docs/source/images/CTMRG_Absorption_U_C1.pdf b/data/docs/source/images/CTMRG_Absorption_U_C1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..a61f2262374e1aef47c023f3b2195ef802b99907 Binary files /dev/null and b/data/docs/source/images/CTMRG_Absorption_U_C1.pdf differ diff --git a/data/docs/source/images/CTMRG_Absorption_U_C1.svg b/data/docs/source/images/CTMRG_Absorption_U_C1.svg new file mode 100644 index 0000000000000000000000000000000000000000..f7d2fae4d683041a4ef18cecd5bf0fb1afdf975b --- /dev/null +++ b/data/docs/source/images/CTMRG_Absorption_U_C1.svg @@ -0,0 +1,556 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/data/docs/source/images/CTMRG_Absorption_U_C1.tex b/data/docs/source/images/CTMRG_Absorption_U_C1.tex new file mode 100644 index 0000000000000000000000000000000000000000..256f6712ccd29630bc0a6011c778a5e7f555674f --- /dev/null +++ b/data/docs/source/images/CTMRG_Absorption_U_C1.tex @@ -0,0 +1,77 @@ +\documentclass[tikz]{standalone} + +\usepackage{amsfonts} +\usepackage{amsmath} +\usepackage{braket} + +\usepackage{tikz} +\usetikzlibrary{calc, decorations, positioning} + +% load TikZ grafic definitions +%\input{gfx_TikZ} + +% main document +\begin{document} + + \begin{tikzpicture}[] + + % contant definitions + \def\tensorSize{0.2} + + % tensor network contraction + \begin{scope} + + % iPEPS network coordinates + \coordinate (PN) at (+0.0, +0.5); + \coordinate (PC) at (+0.0, -0.5); + + % CTMRG network coordinates + \coordinate (C1) at (-0.5, +1.5); + \coordinate (T1) at (+1.5, +1.5); + \coordinate (C2) at (+3.5, +1.5); + \coordinate (T2) at (+2.0, +0.0); + \coordinate (C3) at (+0.5, -1.5); + \coordinate (T3) at (-1.5, -1.5); + \coordinate (C4) at (-3.5, -1.5); + \coordinate (T4) at (-2.0, -0.0); + + % projector P_{UR} + \begin{scope}[shift = {(+1.50, +0.50)}] + \coordinate (PRU) at (+0.00, +1.00); + \coordinate (PRM) at (-1.00, -0.00); + \coordinate (PRD) at (-2.00, -1.00); + \coordinate (PRR) at (+0.00, +0.00); + \node[] at (-0.00, -1.00) {$P_\text{U(R)}^{[x, y - 1]}$}; + \end{scope} + + % tensor labels + \node[above = 0.25] at (C1) {$C_{1}^{[x, y]}$}; + \node[left = 0.25] at (T4) {$T_{4}^{[x, y]}$}; + + % external links + \draw[ultra thick] (PRR) to ($(PRR) + (+1.50, +0.00)$) node at ($(PRR) + (+2.00, +0.00)$) {$-2$}; + \draw[ultra thick] (T4) to ($(T4) + (-0.75, -0.75)$) node at ($(T4) + (-1.00, -1.00)$) {$-1$}; + + % projector + \draw[thick, fill = gray!25] (PRR) to (PRU) to (PRD) -- cycle; + + % internal links + \draw[ultra thick] (PRU) -- (C1) node[above] at ($(C1)!0.5!(PRU)$) {$2$}; + \draw[ultra thick] (C1) -- (T4) node [midway, left = 0.25] {$1$}; + \draw[thick] (PRM) to [out = 180, in = 0] (T4) node[above] at ($(PRM)!0.5!(T4)$) {$3$}; + \draw[thick] (PRD) to [out = 180, in = 0] (T4) node[below] at ($(PRD)!0.5!(T4)$) {$4$}; + + % CTMRG tensors + \foreach \tensor in {T4, C1} { + \draw[thick,black,fill = gray] (\tensor) circle (\tensorSize); + } + + \end{scope} + + \end{tikzpicture} + +\end{document} +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: diff --git a/data/docs/source/images/CTMRG_Absorption_U_C2.pdf b/data/docs/source/images/CTMRG_Absorption_U_C2.pdf new file mode 100644 index 0000000000000000000000000000000000000000..a42cd9221257ef43f7292bd9e25cd12dd3dd3a7a Binary files /dev/null and b/data/docs/source/images/CTMRG_Absorption_U_C2.pdf differ diff --git a/data/docs/source/images/CTMRG_Absorption_U_C2.svg b/data/docs/source/images/CTMRG_Absorption_U_C2.svg new file mode 100644 index 0000000000000000000000000000000000000000..3c442ebf5c36c42dc8f45789dff4312a31f53dc4 --- /dev/null +++ b/data/docs/source/images/CTMRG_Absorption_U_C2.svg @@ -0,0 +1,555 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/data/docs/source/images/CTMRG_Absorption_U_C2.tex b/data/docs/source/images/CTMRG_Absorption_U_C2.tex new file mode 100644 index 0000000000000000000000000000000000000000..110b31cd3c62ac40cf8bea741ee27802d14d038a --- /dev/null +++ b/data/docs/source/images/CTMRG_Absorption_U_C2.tex @@ -0,0 +1,77 @@ +\documentclass[tikz]{standalone} + +\usepackage{amsfonts} +\usepackage{amsmath} +\usepackage{braket} + +\usepackage{tikz} +\usetikzlibrary{calc, decorations, positioning} + +% load TikZ grafic definitions +%\input{gfx_TikZ} + +% main document +\begin{document} + + \begin{tikzpicture}[] + + % contant definitions + \def\tensorSize{0.2} + + % tensor network contraction + \begin{scope} + + % iPEPS network coordinates + \coordinate (PN) at (+0.0, +0.5); + \coordinate (PC) at (+0.0, -0.5); + + % CTMRG network coordinates + \coordinate (C1) at (-0.5, +1.5); + \coordinate (T1) at (+1.5, +1.5); + \coordinate (C2) at (+3.5, +1.5); + \coordinate (T2) at (+2.0, +0.0); + \coordinate (C3) at (+0.5, -1.5); + \coordinate (T3) at (-1.5, -1.5); + \coordinate (C4) at (-3.5, -1.5); + \coordinate (T4) at (-2.0, -0.0); + + % projector P_{UL} + \begin{scope}[shift = {(-1.50, +0.50)}] + \coordinate (PLL) at (+0.00, +0.00); + \coordinate (PLU) at (+2.00, +1.00); + \coordinate (PLM) at (+1.00, +0.00); + \coordinate (PLD) at (+0.00, -1.00); + \node[] at (+0.00, +1.00) {$P_\text{U(L)}^{[x, y]}$}; + \end{scope} + + % tensor labels + \node[above = 0.25] at (C2) {$C_{2}^{[x, y]}$}; + \node[right = 0.25] at (T2) {$T_{2}^{[x, y]}$}; + + % external links + \draw[ultra thick] (PLL) to ($(PLL) + (-1.50, +0.00)$) node at ($(PLL) + (-2.00, +0.00)$) {$-1$}; + \draw[ultra thick] (T2) to ($(T2) + (-0.75, -0.75)$) node at ($(T2) + (-1.00, -1.00)$) {$-2$}; + + % projector + \draw[thick, fill = gray!25] (PLL) to (PLU) to (PLD) -- cycle; + + % internal links + \draw[ultra thick] (C2) -- (PLU) node[above] at ($(C2)!0.5!(PLU)$) {$2$}; + \draw[ultra thick] (C2) -- (T2) node [midway, right = 0.25] {$1$}; + \draw[thick] (T2) to [out = 180, in = 0] (PLM) node[above] at ($(T2)!0.5!(PLM)$) {$3$}; + \draw[thick] (T2) to [out = 180, in = 0] (PLD) node[below] at ($(T2)!0.5!(PLD)$) {$4$}; + + % CTMRG tensors + \foreach \tensor in {C2, T2} { + \draw[thick,black,fill = gray] (\tensor) circle (\tensorSize); + } + + \end{scope} + + \end{tikzpicture} + +\end{document} +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: diff --git a/data/docs/source/images/CTMRG_Absorption_U_T1.pdf b/data/docs/source/images/CTMRG_Absorption_U_T1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..7186848d78b783487d29333731b9453bb67b278a Binary files /dev/null and b/data/docs/source/images/CTMRG_Absorption_U_T1.pdf differ diff --git a/data/docs/source/images/CTMRG_Absorption_U_T1.svg b/data/docs/source/images/CTMRG_Absorption_U_T1.svg new file mode 100644 index 0000000000000000000000000000000000000000..8a534dbb24fd004503462a44c31e45dbb8a4ab38 --- /dev/null +++ b/data/docs/source/images/CTMRG_Absorption_U_T1.svg @@ -0,0 +1,777 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/data/docs/source/images/CTMRG_Absorption_U_T1.tex b/data/docs/source/images/CTMRG_Absorption_U_T1.tex new file mode 100644 index 0000000000000000000000000000000000000000..7e939543d726a2e43da06194fc59d29f38deaa47 --- /dev/null +++ b/data/docs/source/images/CTMRG_Absorption_U_T1.tex @@ -0,0 +1,99 @@ +\documentclass[tikz]{standalone} + +\usepackage{amsfonts} +\usepackage{amsmath} +\usepackage{braket} + +\usepackage{tikz} +\usetikzlibrary{calc, decorations, positioning} + +% load TikZ grafic definitions +%\input{gfx_TikZ} + +% main document +\begin{document} + + \begin{tikzpicture}[] + + % contant definitions + \def\tensorSize{0.2} + + % tensor network contraction + \begin{scope}[shift = {(+2.0, -0.5)}] + + % iPEPS network coordinates + \coordinate (PN) at (+0.0, +0.5); + \coordinate (PC) at (+0.0, -0.5); + + % CTMRG network coordinates + \coordinate (C1) at (-0.5, +1.5); + \coordinate (T1) at (+1.5, +1.5); + \coordinate (C2) at (+3.5, +1.5); + \coordinate (T2) at (+2.0, +0.0); + \coordinate (C3) at (+0.5, -1.5); + \coordinate (T3) at (-1.5, -1.5); + \coordinate (C4) at (-3.5, -1.5); + \coordinate (T4) at (-2.0, -0.0); + + % projector P_{UL} + \begin{scope}[shift = {(-2.50, +0.50)}] + \coordinate (PLL) at (+0.00, +0.00); + \coordinate (PLU) at (+2.00, +1.00); + \coordinate (PLM) at (+1.00, +0.00); + \coordinate (PLD) at (+0.00, -1.00); + \node[] at (+0.00, +1.00) {$\rho_\text{U(L)}^{[x, y - 1]}$}; + \end{scope} + + % projector P_{UR} + \begin{scope}[shift = {(+3.50, +0.50)}] + \coordinate (PRU) at (+0.00, +1.00); + \coordinate (PRM) at (-1.00, -0.00); + \coordinate (PRD) at (-2.00, -1.00); + \coordinate (PRR) at (+0.00, +0.00); + \node[] at (-0.00, -1.00) {$\rho_\text{U(R)}^{[x, y]}$}; + \end{scope} + + % tensor labels + \node at ($(T1) + (+0.75, +0.75)$) {$T_1^{[x, y]}$}; + + % external links + \draw[thick] (PN) to ($(PN) + (-1.50, -1.50)$) node at ($(PN) + (-2.00, -2.00)$) {$-2$}; + \draw[thick] (PC) to ($(PC) + (-1.50, -1.50)$) node at ($(PC) + (-2.00, -2.00)$) {$-3$}; + \draw[ultra thick] (PLL) to ($(PLL) + (-1.50, -0.00)$) node at ($(PLL) + (-2.00, -0.00)$) {$-1$}; + \draw[ultra thick] (PRR) to ($(PRR) + (+1.50, +0.00)$) node at ($(PRR) + (+2.00, +0.00)$) {$-4$}; + + % projectors + \draw[thick, fill = gray!25] (PLL) to (PLU) to (PLD) -- cycle; + \draw[thick, fill = gray!25] (PRR) to (PRU) to (PRD) -- cycle; + + % internal links + \draw[ultra thick] (T1) -- (PLU) node[above] at ($(T1)!0.5!(PLU)$) {$1$}; + \draw[ultra thick] (T1) -- (PRU) node[above] at ($(T1)!0.5!(PRU)$) {$7$}; + \draw[thick] (PN) to [out = 180, in = 0] (PLM) node[above] at ($(PN)!0.5!(PLM)$) {$3$}; + \draw[thick] (PRM) to [out = 180, in = 0] (PN) node[above] at ($(PRM)!0.3!(PN)$) {$8$}; + \draw[thick] (PC) to [out = 180, in = 0] (PLD) node[above] at ($(PC)!0.7!(PLD)$) {$5$}; + \draw[thick] (PRD) to [out = 180, in = 0] (PC) node[above] at ($(PRD)!0.5!(PC)$) {$9$}; + \draw[thick] (T1) to [out = 225, in = 45] (PC) node[right] at ($(T1)!0.3!(PC)$) {$4$}; + \draw[thick] (T1) to [out = 225, in = 45] (PN) node[above] at ($(T1)!0.7!(PN)$) {$2$}; + \draw[thick] (PN) -- (PC) node [midway, right] {$6$}; + + % CTMRG tensors + \foreach \tensor in {T1} { + \draw[thick,black,fill = gray] (\tensor) circle (\tensorSize); + } + + % iPEPS tensors + \foreach \tensor in {PN, PC} { + \draw[thick,black,fill = blue] (\tensor) circle (\tensorSize); + } + + \end{scope} + + \end{tikzpicture} + +\end{document} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: diff --git a/data/docs/source/images/Makefile b/data/docs/source/images/Makefile new file mode 100644 index 0000000000000000000000000000000000000000..0c364bad11f907520d73b10ba2ed7c730da9b95a --- /dev/null +++ b/data/docs/source/images/Makefile @@ -0,0 +1,27 @@ +#!/usr/bin/make -f + +SRCS := $(wildcard *.tex) +PDFS := $(SRCS:%.tex=%.pdf) +SVGS := $(SRCS:%.tex=%.svg) + +AUXS := $(SRCS:%.tex=%.aux) +TEXLOGS := $(SRCS:%.tex=%.log) + +all: ${PDFS} ${SVGS} logo.png + +%.pdf: %.tex + pdflatex "$<" + +%.svg: %.pdf + inkscape --pdf-poppler "$<" -o "$@" + +%.png: %.pdf + inkscape --pdf-poppler "$<" --export-dpi=300 --export-png="$@" + +texauxclean: + rm -f ${AUXS} + rm -f ${TEXLOGS} + +clean: texauxclean + rm -f ${PDFS} + rm -f ${SVGS} diff --git a/data/docs/source/images/ctmrg_bottom_left.pdf b/data/docs/source/images/ctmrg_bottom_left.pdf new file mode 100644 index 0000000000000000000000000000000000000000..5c2a2e073647e53c374bed5dc26de255dad59c6f Binary files /dev/null and b/data/docs/source/images/ctmrg_bottom_left.pdf differ diff --git a/data/docs/source/images/ctmrg_bottom_left.svg b/data/docs/source/images/ctmrg_bottom_left.svg new file mode 100644 index 0000000000000000000000000000000000000000..34fc3fadad083815d011911dd87950db7d940edb --- /dev/null +++ b/data/docs/source/images/ctmrg_bottom_left.svg @@ -0,0 +1,662 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/data/docs/source/images/ctmrg_bottom_left.tex b/data/docs/source/images/ctmrg_bottom_left.tex new file mode 100644 index 0000000000000000000000000000000000000000..6ad7d4ef136bd550879f3db6d5f681025e5afb40 --- /dev/null +++ b/data/docs/source/images/ctmrg_bottom_left.tex @@ -0,0 +1,68 @@ +\documentclass[tikz]{standalone} + +\usepackage{amsfonts} +\usepackage{amsmath} +\usepackage{braket} + +\usepackage{tikz} +\usetikzlibrary{arrows, arrows.meta, calc, decorations, positioning} + +% load TikZ grafic definitions +%\input{gfx_TikZ} + +% main document +\begin{document} + + \begin{tikzpicture}[] + + \def\tensorSize{0.2} + + \begin{scope} + + % label + \node at (-3.5,0) {\large$\rho_\text{DL}^{[x+1,y]}$}; + + % network corrdinates + \coordinate (PN) at (+0.0, +0.5); + \coordinate (PC) at (+0.0, -0.5); + \coordinate (T3) at (-1.5, -1.5); + \coordinate (C4) at (-3.5, -1.5); + \coordinate (T4) at (-2.0, -0.0); + + % external links + \draw[ultra thick] ($(T3) + (+1.50, +0.00)$) to (T3) node at ($(T3) + (+2.00, +0.00)$) {$-1$}; + \draw[thick] ($(PC) + (+1.00, +0.00)$) to (PC) node at ($(PC) + (+1.50, +0.00)$) {$-2$}; + \draw[thick] ($(PN) + (+2.00, +0.00)$) to (PN) node at ($(PN) + (+2.50, +0.00)$) {$-3$}; + \draw[ultra thick] ($(T4) + (+1.25, +1.25)$) to (T4) node at ($(T4) + (+1.50, +1.50)$) {$-4$}; + \draw[thick] ($(PN) + (+0.75, +0.75)$) to (PN) node at ($(PN) + (+1.00, +1.00)$) {$-5$}; + \draw[thick] ($(PC) + (+1.75, +1.75)$) to (PC) node at ($(PC) + (+2.00, +2.00)$) {$-6$}; + + % internal links + \draw[ultra thick] (T4) to (C4) node[left = 0.25] at ($(T4)!0.5!(C4)$) {$1$}; + \draw[thick] (PC) to [out = 180, in = 0] (T4) node[below] at ($(PC)!0.7!(T4)$) {$5$}; + \draw[ultra thick] (T3) -- (C4) node [midway, below] {$2$}; + \draw[thick] (PC) to [out = 225, in = 45] (T3) node[below right] at ($(PC)!0.3!(T3)$) {$6$}; + \draw[thick] (PN) to [out = 180, in = 0] (T4) node[above] at ($(PN)!0.3!(T4)$) {$3$}; + \draw[thick] (PN) to [out = 225, in = 45] (T3) node[left] at ($(PN)!0.7!(T3)$) {$4$}; + \draw[thick] (PN) -- (PC) node [midway, right] {$7$}; + + % CTMRG tensors + \foreach \tensor in {T3, C4, T4} { + \draw[thick,black,fill = gray] (\tensor) circle (\tensorSize); + } + + % iPEPS tensors + \foreach \tensor in {PN, PC} { + \draw[thick,black,fill = blue] (\tensor) circle (\tensorSize); + } + + \end{scope} + + \end{tikzpicture} + +\end{document} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: diff --git a/data/docs/source/images/ctmrg_bottom_left_large_d.pdf b/data/docs/source/images/ctmrg_bottom_left_large_d.pdf new file mode 100644 index 0000000000000000000000000000000000000000..a22a210dff8cd132ddaf239d107259e9a8fb6d77 Binary files /dev/null and b/data/docs/source/images/ctmrg_bottom_left_large_d.pdf differ diff --git a/data/docs/source/images/ctmrg_bottom_left_large_d.svg b/data/docs/source/images/ctmrg_bottom_left_large_d.svg new file mode 100644 index 0000000000000000000000000000000000000000..cdf68afa919778a08937ed034c4ff4271f63d136 --- /dev/null +++ b/data/docs/source/images/ctmrg_bottom_left_large_d.svg @@ -0,0 +1,662 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/data/docs/source/images/ctmrg_bottom_left_large_d.tex b/data/docs/source/images/ctmrg_bottom_left_large_d.tex new file mode 100644 index 0000000000000000000000000000000000000000..9b7f7f1ba023b54b2569aee77e8cf76643417e7c --- /dev/null +++ b/data/docs/source/images/ctmrg_bottom_left_large_d.tex @@ -0,0 +1,68 @@ +\documentclass[tikz]{standalone} + +\usepackage{amsfonts} +\usepackage{amsmath} +\usepackage{braket} + +\usepackage{tikz} +\usetikzlibrary{arrows, arrows.meta, calc, decorations, positioning} + +% load TikZ grafic definitions +%\input{gfx_TikZ} + +% main document +\begin{document} + + \begin{tikzpicture}[] + + \def\tensorSize{0.2} + + \begin{scope} + + % label + \node at (-3.5,0) {\large$\rho_\text{DL}^{[x+1,y]}$}; + + % network corrdinates + \coordinate (PN) at (+0.0, +0.5); + \coordinate (PC) at (+0.0, -0.5); + \coordinate (T3) at (-1.5, -1.5); + \coordinate (C4) at (-3.5, -1.5); + \coordinate (T4) at (-2.0, -0.0); + + % external links + \draw[ultra thick] ($(T3) + (+1.50, +0.00)$) to (T3) node at ($(T3) + (+2.00, +0.00)$) {$-1$}; + \draw[thick] ($(PC) + (+1.00, +0.00)$) to (PC) node at ($(PC) + (+1.50, +0.00)$) {$-2$}; + \draw[thick] ($(PN) + (+2.00, +0.00)$) to (PN) node at ($(PN) + (+2.50, +0.00)$) {$-3$}; + \draw[ultra thick] ($(T4) + (+1.25, +1.25)$) to (T4) node at ($(T4) + (+1.50, +1.50)$) {$-4$}; + \draw[thick] ($(PN) + (+0.75, +0.75)$) to (PN) node at ($(PN) + (+1.00, +1.00)$) {$-5$}; + \draw[thick] ($(PC) + (+1.75, +1.75)$) to (PC) node at ($(PC) + (+2.00, +2.00)$) {$-6$}; + + % internal links + \draw[ultra thick] (T4) to (C4) node[left = 0.25] at ($(T4)!0.5!(C4)$) {$1$}; + \draw[thick] (PC) to [out = 180, in = 0] (T4) node[below] at ($(PC)!0.7!(T4)$) {$6$}; + \draw[ultra thick] (T3) -- (C4) node [midway, below] {$2$}; + \draw[thick] (PC) to [out = 225, in = 45] (T3) node[below right] at ($(PC)!0.3!(T3)$) {$7$}; + \draw[thick] (PN) to [out = 180, in = 0] (T4) node[above] at ($(PN)!0.3!(T4)$) {$4$}; + \draw[thick] (PN) to [out = 225, in = 45] (T3) node[left] at ($(PN)!0.7!(T3)$) {$5$}; + \draw[thick] (PN) -- (PC) node [midway, right] {$3$}; + + % CTMRG tensors + \foreach \tensor in {T3, C4, T4} { + \draw[thick,black,fill = gray] (\tensor) circle (\tensorSize); + } + + % iPEPS tensors + \foreach \tensor in {PN, PC} { + \draw[thick,black,fill = blue] (\tensor) circle (\tensorSize); + } + + \end{scope} + + \end{tikzpicture} + +\end{document} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: diff --git a/data/docs/source/images/ctmrg_bottom_right.pdf b/data/docs/source/images/ctmrg_bottom_right.pdf new file mode 100644 index 0000000000000000000000000000000000000000..e3055380792839d55ca72a4989d9788074da5303 Binary files /dev/null and b/data/docs/source/images/ctmrg_bottom_right.pdf differ diff --git a/data/docs/source/images/ctmrg_bottom_right.svg b/data/docs/source/images/ctmrg_bottom_right.svg new file mode 100644 index 0000000000000000000000000000000000000000..04f6ec6a7c4c4eaebb968bb08ead4aa8808786be --- /dev/null +++ b/data/docs/source/images/ctmrg_bottom_right.svg @@ -0,0 +1,672 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/data/docs/source/images/ctmrg_bottom_right.tex b/data/docs/source/images/ctmrg_bottom_right.tex new file mode 100644 index 0000000000000000000000000000000000000000..1214b93cb1ab35c4ce26a107b75913e2b9ea1a14 --- /dev/null +++ b/data/docs/source/images/ctmrg_bottom_right.tex @@ -0,0 +1,68 @@ +\documentclass[tikz]{standalone} + +\usepackage{amsfonts} +\usepackage{amsmath} +\usepackage{braket} + +\usepackage{tikz} +\usetikzlibrary{arrows, arrows.meta, calc, decorations, positioning} + +% load TikZ grafic definitions +%\input{gfx_TikZ} + +% main document +\begin{document} + + \begin{tikzpicture}[] + + \def\tensorSize{0.2} + + \begin{scope} + + % label + \node at (+3.5,0) {\large$\rho_\text{DR}^{[x+1,y+1]}$}; + + % network corrdinates + \coordinate (PN) at (+0.0, +0.5); + \coordinate (PC) at (+0.0, -0.5); + \coordinate (T2) at (+2.0, -0.0); + \coordinate (C3) at (+0.5, -1.5); + \coordinate (T3) at (-1.5, -1.5); + + % external links + \draw[ultra thick] ($(T2) + (+1.25, +1.25)$) to (T2) node at ($(T2) + (+1.50, +1.50)$) {$-1$}; + \draw[thick] ($(PC) + (+1.75, +1.75)$) to (PC) node at ($(PC) + (+2.00, +2.00)$) {$-2$}; + \draw[thick] ($(PN) + (+0.75, +0.75)$) to (PN) node at ($(PN) + (+1.00, +1.00)$) {$-3$}; + \draw[ultra thick] ($(T3) + (-1.50, +0.00)$) to (T3) node at ($(T3) + (-2.00, +0.00)$) {$-4$}; + \draw[thick] (PC) to ($(PC) + (-2.00, +0.00)$) node at ($(PC) + (-2.50, +0.00)$) {$-5$}; + \draw[thick] (PN) to ($(PN) + (-1.00, +0.00)$) node at ($(PN) + (-1.50, +0.00)$) {$-6$}; + + % internal links + \draw[ultra thick] (T2) to (C3) node[right = 0.25] at ($(T2)!0.5!(C3)$) {$2$}; + \draw[thick] (T2) to [out = 180, in = 0] (PC) node[below] at ($(T2)!0.7!(PC)$) {$6$}; + \draw[ultra thick] (C3) -- (T3) node [midway, below] {$1$}; + \draw[thick] (PC) to [out = 225, in = 45] (T3) node[below right] at ($(PC)!0.3!(T3)$) {$5$}; + \draw[thick] (T2) to [out = 180, in = 0] (PN) node[above] at ($(T2)!0.3!(PN)$) {$4$}; + \draw[thick] (PN) to [out = 225, in = 45] (T3) node[left] at ($(PN)!0.7!(T3)$) {$3$}; + \draw[thick] (PN) -- (PC) node [midway, right] {$7$}; + + % CTMRG tensors + \foreach \tensor in {T2, C3, T3} { + \draw[thick,black,fill = gray] (\tensor) circle (\tensorSize); + } + + % iPEPS tensors + \foreach \tensor in {PN, PC} { + \draw[thick,black,fill = blue] (\tensor) circle (\tensorSize); + } + + \end{scope} + + \end{tikzpicture} + +\end{document} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: diff --git a/data/docs/source/images/ctmrg_bottom_right_large_d.pdf b/data/docs/source/images/ctmrg_bottom_right_large_d.pdf new file mode 100644 index 0000000000000000000000000000000000000000..4c6520e22a82e7ac03b88a1d9df3d90c1dad6974 Binary files /dev/null and b/data/docs/source/images/ctmrg_bottom_right_large_d.pdf differ diff --git a/data/docs/source/images/ctmrg_bottom_right_large_d.svg b/data/docs/source/images/ctmrg_bottom_right_large_d.svg new file mode 100644 index 0000000000000000000000000000000000000000..cfebd409327c558bb93e0acf5266197f145d9620 --- /dev/null +++ b/data/docs/source/images/ctmrg_bottom_right_large_d.svg @@ -0,0 +1,672 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/data/docs/source/images/ctmrg_bottom_right_large_d.tex b/data/docs/source/images/ctmrg_bottom_right_large_d.tex new file mode 100644 index 0000000000000000000000000000000000000000..22347629a1806d5b0595a55a7a15a9f9999fbff5 --- /dev/null +++ b/data/docs/source/images/ctmrg_bottom_right_large_d.tex @@ -0,0 +1,68 @@ +\documentclass[tikz]{standalone} + +\usepackage{amsfonts} +\usepackage{amsmath} +\usepackage{braket} + +\usepackage{tikz} +\usetikzlibrary{arrows, arrows.meta, calc, decorations, positioning} + +% load TikZ grafic definitions +%\input{gfx_TikZ} + +% main document +\begin{document} + + \begin{tikzpicture}[] + + \def\tensorSize{0.2} + + \begin{scope} + + % label + \node at (+3.5,0) {\large$\rho_\text{DR}^{[x+1,y+1]}$}; + + % network corrdinates + \coordinate (PN) at (+0.0, +0.5); + \coordinate (PC) at (+0.0, -0.5); + \coordinate (T2) at (+2.0, -0.0); + \coordinate (C3) at (+0.5, -1.5); + \coordinate (T3) at (-1.5, -1.5); + + % external links + \draw[ultra thick] ($(T2) + (+1.25, +1.25)$) to (T2) node at ($(T2) + (+1.50, +1.50)$) {$-1$}; + \draw[thick] ($(PC) + (+1.75, +1.75)$) to (PC) node at ($(PC) + (+2.00, +2.00)$) {$-2$}; + \draw[thick] ($(PN) + (+0.75, +0.75)$) to (PN) node at ($(PN) + (+1.00, +1.00)$) {$-3$}; + \draw[ultra thick] ($(T3) + (-1.50, +0.00)$) to (T3) node at ($(T3) + (-2.00, +0.00)$) {$-4$}; + \draw[thick] (PC) to ($(PC) + (-2.00, +0.00)$) node at ($(PC) + (-2.50, +0.00)$) {$-5$}; + \draw[thick] (PN) to ($(PN) + (-1.00, +0.00)$) node at ($(PN) + (-1.50, +0.00)$) {$-6$}; + + % internal links + \draw[ultra thick] (T2) to (C3) node[right = 0.25] at ($(T2)!0.5!(C3)$) {$2$}; + \draw[thick] (T2) to [out = 180, in = 0] (PC) node[below] at ($(T2)!0.7!(PC)$) {$7$}; + \draw[ultra thick] (C3) -- (T3) node [midway, below] {$1$}; + \draw[thick] (PC) to [out = 225, in = 45] (T3) node[below right] at ($(PC)!0.3!(T3)$) {$6$}; + \draw[thick] (T2) to [out = 180, in = 0] (PN) node[above] at ($(T2)!0.3!(PN)$) {$5$}; + \draw[thick] (PN) to [out = 225, in = 45] (T3) node[left] at ($(PN)!0.7!(T3)$) {$4$}; + \draw[thick] (PN) -- (PC) node [midway, right] {$3$}; + + % CTMRG tensors + \foreach \tensor in {T2, C3, T3} { + \draw[thick,black,fill = gray] (\tensor) circle (\tensorSize); + } + + % iPEPS tensors + \foreach \tensor in {PN, PC} { + \draw[thick,black,fill = blue] (\tensor) circle (\tensorSize); + } + + \end{scope} + + \end{tikzpicture} + +\end{document} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: diff --git a/data/docs/source/images/ctmrg_top_left.pdf b/data/docs/source/images/ctmrg_top_left.pdf new file mode 100644 index 0000000000000000000000000000000000000000..a55810ee7ab5a707beb24b769603964392f55f97 Binary files /dev/null and b/data/docs/source/images/ctmrg_top_left.pdf differ diff --git a/data/docs/source/images/ctmrg_top_left.svg b/data/docs/source/images/ctmrg_top_left.svg new file mode 100644 index 0000000000000000000000000000000000000000..b3f96c42cf1625546b4166497105889ac002d2ba --- /dev/null +++ b/data/docs/source/images/ctmrg_top_left.svg @@ -0,0 +1,600 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/data/docs/source/images/ctmrg_top_left.tex b/data/docs/source/images/ctmrg_top_left.tex new file mode 100644 index 0000000000000000000000000000000000000000..474e0d44af4e10a8977aee0ef5e2e50e978285f7 --- /dev/null +++ b/data/docs/source/images/ctmrg_top_left.tex @@ -0,0 +1,69 @@ +\documentclass[tikz]{standalone} + +\usepackage{amsfonts} +\usepackage{amsmath} +\usepackage{braket} + +\usepackage{tikz} +\usetikzlibrary{arrows, arrows.meta, calc, decorations, positioning} + +% load TikZ grafic definitions +%\input{gfx_TikZ} + +% main document +\begin{document} + + \begin{tikzpicture}[] + + \def\tensorSize{0.2} + + \begin{scope}[shift = {(-3, +2)}] + + % label + \node at (-3.5,0) {\large$\rho_\text{UL}^{[x,y]}$}; + + % network corrdinates + \coordinate (PN) at (+0.0, +0.5); + \coordinate (PC) at (+0.0, -0.5); + \coordinate (T4) at (-2.0, -0.0); + \coordinate (C1) at (-0.5, +1.5); + \coordinate (T1) at (+1.5, +1.5); + + % external links + \draw[ultra thick] (T4) to ($(T4) + (-1.25, -1.25)$) node at ($(T4) + (-1.50, -1.50)$) {$-1$}; + \draw[thick] (PN) to ($(PN) + (-1.75, -1.75)$) node at ($(PN) + (-2.00, -2.00)$) {$-2$}; + \draw[thick] (PC) to ($(PC) + (-0.75, -0.75)$) node at ($(PC) + (-1.00, -1.00)$) {$-3$}; + \draw[ultra thick] (T1) to ($(T1) + (+1.50, +0.00)$) node at ($(T1) + (+2.00, +0.00)$) {$-4$}; + \draw[thick] (PN) to ($(PN) + (+2.00, +0.00)$) node at ($(PN) + (+2.50, +0.00)$) {$-5$}; + \draw[thick] (PC) to ($(PC) + (+1.00, +0.00)$) node at ($(PC) + (+1.50, +0.00)$) {$-6$}; + + + % internal links + \draw[ultra thick] (C1) -- (T4) node[left = 0.25] at ($(C1)!0.5!(T4)$) {$1$}; + \draw[thick] (T4) to [out = 0, in = 180] (PC) node[below] at ($(T4)!0.3!(PC)$) {$5$}; + \draw[ultra thick] (C1) -- (T1) node [midway, above] {$2$}; + \draw[thick] (T1) to [out = 225, in = 45] (PC) node[right] at ($(T1)!0.3!(PC)$) {$6$}; + \draw[thick] (T4) to [out = 0, in = 180] (PN) node[above] at ($(T4)!0.7!(PN)$) {$3$}; + \draw[thick] (T1) to [out = 225, in = 45] (PN) node[above left] at ($(T1)!0.7!(PN)$) {$4$}; + \draw[thick] (PN) -- (PC) node [midway, right] {$7$}; + + % CTMRG tensors + \foreach \tensor in {T4, C1, T1} { + \draw[thick,black,fill = gray] (\tensor) circle (\tensorSize); + } + + % iPEPS tensors + \foreach \tensor in {PN, PC} { + \draw[thick,black,fill = blue] (\tensor) circle (\tensorSize); + } + + \end{scope} + + \end{tikzpicture} + +\end{document} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: diff --git a/data/docs/source/images/ctmrg_top_left_large_d.pdf b/data/docs/source/images/ctmrg_top_left_large_d.pdf new file mode 100644 index 0000000000000000000000000000000000000000..81c882930c3456d3524d33431c7fef8747d34131 Binary files /dev/null and b/data/docs/source/images/ctmrg_top_left_large_d.pdf differ diff --git a/data/docs/source/images/ctmrg_top_left_large_d.svg b/data/docs/source/images/ctmrg_top_left_large_d.svg new file mode 100644 index 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TikZ grafic definitions +%\input{gfx_TikZ} + +% main document +\begin{document} + + \begin{tikzpicture}[] + + \def\tensorSize{0.2} + + \begin{scope}[shift = {(-3, +2)}] + + % label + \node at (-3.5,0) {\large$\rho_\text{UL}^{[x,y]}$}; + + % network corrdinates + \coordinate (PN) at (+0.0, +0.5); + \coordinate (PC) at (+0.0, -0.5); + \coordinate (T4) at (-2.0, -0.0); + \coordinate (C1) at (-0.5, +1.5); + \coordinate (T1) at (+1.5, +1.5); + + % external links + \draw[ultra thick] (T4) to ($(T4) + (-1.25, -1.25)$) node at ($(T4) + (-1.50, -1.50)$) {$-1$}; + \draw[thick] (PN) to ($(PN) + (-1.75, -1.75)$) node at ($(PN) + (-2.00, -2.00)$) {$-2$}; + \draw[thick] (PC) to ($(PC) + (-0.75, -0.75)$) node at ($(PC) + (-1.00, -1.00)$) {$-3$}; + \draw[ultra thick] (T1) to ($(T1) + (+1.50, +0.00)$) node at ($(T1) + (+2.00, +0.00)$) {$-4$}; + \draw[thick] (PN) to ($(PN) + (+2.00, +0.00)$) node at ($(PN) + (+2.50, +0.00)$) {$-5$}; + \draw[thick] (PC) to ($(PC) + (+1.00, +0.00)$) node at ($(PC) + (+1.50, +0.00)$) {$-6$}; + + + % internal links + \draw[ultra thick] (C1) -- (T4) node[left = 0.25] at ($(C1)!0.5!(T4)$) {$1$}; + \draw[thick] (T4) to [out = 0, in = 180] (PC) node[below] at ($(T4)!0.3!(PC)$) {$6$}; + \draw[ultra thick] (C1) -- (T1) node [midway, above] {$2$}; + \draw[thick] (T1) to [out = 225, in = 45] (PC) node[right] at ($(T1)!0.3!(PC)$) {$7$}; + \draw[thick] (T4) to [out = 0, in = 180] (PN) node[above] at ($(T4)!0.7!(PN)$) {$4$}; + \draw[thick] (T1) to [out = 225, in = 45] (PN) node[above left] at ($(T1)!0.7!(PN)$) {$5$}; + \draw[thick] (PN) -- (PC) node [midway, right] {$3$}; + + % CTMRG tensors + \foreach \tensor in {T4, C1, T1} { + \draw[thick,black,fill = gray] (\tensor) circle (\tensorSize); + } + + % iPEPS tensors + \foreach \tensor in {PN, PC} { + \draw[thick,black,fill = blue] (\tensor) circle (\tensorSize); + } + + \end{scope} + + \end{tikzpicture} + +\end{document} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: diff --git a/data/docs/source/images/ctmrg_top_right.pdf b/data/docs/source/images/ctmrg_top_right.pdf new file mode 100644 index 0000000000000000000000000000000000000000..79b66ae1d29360d7a3b76079e0551f7d43f3c9c4 Binary files /dev/null and b/data/docs/source/images/ctmrg_top_right.pdf differ diff --git a/data/docs/source/images/ctmrg_top_right.svg b/data/docs/source/images/ctmrg_top_right.svg new file mode 100644 index 0000000000000000000000000000000000000000..3e5e7fe623b91254957800d776694c3509873dd8 --- /dev/null +++ b/data/docs/source/images/ctmrg_top_right.svg @@ -0,0 +1,633 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/data/docs/source/images/ctmrg_top_right.tex b/data/docs/source/images/ctmrg_top_right.tex new file mode 100644 index 0000000000000000000000000000000000000000..3fde7c11f66280a8539dec4a23c5281b2b56db10 --- /dev/null +++ b/data/docs/source/images/ctmrg_top_right.tex @@ -0,0 +1,69 @@ +\documentclass[tikz]{standalone} + +\usepackage{amsfonts} +\usepackage{amsmath} +\usepackage{braket} + +\usepackage{tikz} +\usetikzlibrary{arrows, arrows.meta, calc, decorations, positioning} + +% load TikZ grafic definitions +%\input{gfx_TikZ} + +% main document +\begin{document} + + \begin{tikzpicture}[] + + \def\tensorSize{0.2} + + \begin{scope}[shift = {(+3, +2)}] + + % label + \node at (+3.5,0) {\large$\rho_\text{UR}^{[x,y + 1]}$}; + + % network corrdinates + \coordinate (PN) at (+0.0, +0.5); + \coordinate (PC) at (+0.0, -0.5); + \coordinate (T1) at (+1.5, +1.5); + \coordinate (C2) at (+3.5, +1.5); + \coordinate (T2) at (+2.0, -0.0); + + % external links + \draw[ultra thick] (T1) to ($(T1) + (-1.50, +0.00)$) node at ($(T1) + (-2.00, +0.00)$) {$-1$}; + \draw[thick] (PN) to ($(PN) + (-1.00, +0.00)$) node at ($(PN) + (-1.50, +0.00)$) {$-2$}; + \draw[thick] (PC) to ($(PC) + (-2.00, +0.00)$) node at ($(PC) + (-2.50, +0.00)$) {$-3$}; + \draw[ultra thick] (T2) to ($(T2) + (-1.25, -1.25)$) node at ($(T2) + (-1.50, -1.50)$) {$-4$}; + \draw[thick] (PC) to ($(PC) + (-0.75, -0.75)$) node at ($(PC) + (-1.00, -1.00)$) {$-5$}; + \draw[thick] (PN) to ($(PN) + (-1.75, -1.75)$) node at ($(PN) + (-2.00, -2.00)$) {$-6$}; + + + % internal links + \draw[ultra thick] (C2) to (T2) node[right = 0.25] at ($(C2)!0.5!(T2)$) {$2$}; + \draw[thick] (T2) to [out = 180, in = 0] (PC) node[below] at ($(T2)!0.7!(PC)$) {$6$}; + \draw[ultra thick] (C2) -- (T1) node [midway, above] {$1$}; + \draw[thick] (T1) to [out = 225, in = 45] (PC) node[right] at ($(T1)!0.3!(PC)$) {$5$}; + \draw[thick] (T2) to [out = 180, in = 0] (PN) node[above] at ($(T2)!0.3!(PN)$) {$4$}; + \draw[thick] (T1) to [out = 225, in = 45] (PN) node[above left] at ($(T1)!0.7!(PN)$) {$3$}; + \draw[thick] (PN) -- (PC) node [midway, right] {$7$}; + + % CTMRG tensors + \foreach \tensor in {T1, C2, T2} { + \draw[thick,black,fill = gray] (\tensor) circle (\tensorSize); + } + + % iPEPS tensors + \foreach \tensor in {PN, PC} { + \draw[thick,black,fill = blue] (\tensor) circle (\tensorSize); + } + + \end{scope} + + \end{tikzpicture} + +\end{document} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: diff --git a/data/docs/source/images/ctmrg_top_right_large_d.pdf b/data/docs/source/images/ctmrg_top_right_large_d.pdf new file mode 100644 index 0000000000000000000000000000000000000000..b965450f31014a7e3f2d7cca45d2c781dc4bf1ec Binary files /dev/null and b/data/docs/source/images/ctmrg_top_right_large_d.pdf differ diff --git a/data/docs/source/images/ctmrg_top_right_large_d.svg b/data/docs/source/images/ctmrg_top_right_large_d.svg new file mode 100644 index 0000000000000000000000000000000000000000..2a7557f0c5700f2978b9d72b290452d812945bc3 --- /dev/null +++ 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+\begin{document} + + \begin{tikzpicture}[] + + \def\tensorSize{0.2} + + \begin{scope}[shift = {(+3, +2)}] + + % label + \node at (+3.5,0) {\large$\rho_\text{UR}^{[x,y + 1]}$}; + + % network corrdinates + \coordinate (PN) at (+0.0, +0.5); + \coordinate (PC) at (+0.0, -0.5); + \coordinate (T1) at (+1.5, +1.5); + \coordinate (C2) at (+3.5, +1.5); + \coordinate (T2) at (+2.0, -0.0); + + % external links + \draw[ultra thick] (T1) to ($(T1) + (-1.50, +0.00)$) node at ($(T1) + (-2.00, +0.00)$) {$-1$}; + \draw[thick] (PN) to ($(PN) + (-1.00, +0.00)$) node at ($(PN) + (-1.50, +0.00)$) {$-2$}; + \draw[thick] (PC) to ($(PC) + (-2.00, +0.00)$) node at ($(PC) + (-2.50, +0.00)$) {$-3$}; + \draw[ultra thick] (T2) to ($(T2) + (-1.25, -1.25)$) node at ($(T2) + (-1.50, -1.50)$) {$-4$}; + \draw[thick] (PC) to ($(PC) + (-0.75, -0.75)$) node at ($(PC) + (-1.00, -1.00)$) {$-5$}; + \draw[thick] (PN) to ($(PN) + (-1.75, -1.75)$) node at ($(PN) + (-2.00, -2.00)$) {$-6$}; + + + % internal links + \draw[ultra thick] (C2) to (T2) node[right = 0.25] at ($(C2)!0.5!(T2)$) {$2$}; + \draw[thick] (T2) to [out = 180, in = 0] (PC) node[below] at ($(T2)!0.7!(PC)$) {$7$}; + \draw[ultra thick] (C2) -- (T1) node [midway, above] {$1$}; + \draw[thick] (T1) to [out = 225, in = 45] (PC) node[right] at ($(T1)!0.3!(PC)$) {$6$}; + \draw[thick] (T2) to [out = 180, in = 0] (PN) node[above] at ($(T2)!0.3!(PN)$) {$5$}; + \draw[thick] (T1) to [out = 225, in = 45] (PN) node[above left] at ($(T1)!0.7!(PN)$) {$4$}; + \draw[thick] (PN) -- (PC) node [midway, right] {$3$}; + + % CTMRG tensors + \foreach \tensor in {T1, C2, T2} { + \draw[thick,black,fill = gray] (\tensor) circle (\tensorSize); + } + + % iPEPS tensors + \foreach \tensor in {PN, PC} { + \draw[thick,black,fill = blue] (\tensor) circle (\tensorSize); + } + + \end{scope} + + \end{tikzpicture} + +\end{document} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: diff --git a/data/docs/source/images/favicon/android-chrome-192x192.png 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a/data/docs/source/images/floret_pentagon_bond_colors.tex b/data/docs/source/images/floret_pentagon_bond_colors.tex new file mode 100644 index 0000000000000000000000000000000000000000..ef24758d12902124d5e2617a91102ec61157d99c --- /dev/null +++ b/data/docs/source/images/floret_pentagon_bond_colors.tex @@ -0,0 +1,151 @@ +\documentclass[tikz]{standalone} + +\usepackage{amsfonts} +\usepackage{amsmath} +\usepackage{braket} + +\usepackage{tikz} +\usetikzlibrary{math, calc, decorations, positioning} + +% load TikZ grafic definitions +%\input{gfx_TikZ} + +% main document +\begin{document} + +\pgfdeclarelayer{v1} % background layer +\pgfdeclarelayer{v2} % foreground layer +\pgfsetlayers{v1,main,v2} % set the order of the layers (main is the standard layer) +\tikzset{ + bonda/.style={black, line width=.65pt}, + bondb/.style={blue!80!white, line width=.65pt}, + bondc/.style={green!80!black, line width=0.65pt}} + +\begin{tikzpicture} + \tikzmath { + \ang0 = 0; + \lb = 0.5; + \la = 2*\lb; + int \sa; + int \sb; + \nt = 1; + for \sa in {-\nt,...,\nt}{ + int \sbmin, \sbmax; + \sbmin = max(-\nt, -\nt-\sa); + \sbmax = min(\nt, \nt-\sa); + for \sb in {\sbmin,...,\sbmax}{ + coordinate \oo; + \oo = (70.89339464913091+\ang0:9.16515138991168*\sa*\lb/2) + + (10.893394649130906+\ang0:9.16515138991168*\sb*\lb/2); + int \i; + for \i in {0,1,2,3,4,5}{ + \angr = 60*\i+\ang0; + \a1 = 0+\angr; + \a2 = 60+\angr; + \a3 = 120+\angr; + \a4 = 180+\angr; + { + \draw[bonda] (\oo) coordinate (oo) coordinate (oo a\sa b\sb) -- + ++(\a1:\la) coordinate (pa \i) coordinate (pa \i a\sa b\sb) + ++ (\a2:\lb) coordinate (pb \i) coordinate (pb \i a\sa b\sb) + ++ (\a3:\lb) coordinate (pc \i) coordinate (pc \i a\sa b\sb) + ++ (\a4:\lb) coordinate (pd \i) coordinate (pd \i a\sa b\sb); + }; + }; + { + + % \draw (pa 0) -- (pb 0) -- (pc 0) -- (pd 0); + % \draw (pa 1) -- (pb 1) -- (pc 1) -- (pd 1); + % \draw (pa 2) -- (pb 2) -- (pc 2); + % \draw (pc 5) -- (pa 0); + \draw[bondb] (pa 0) -- (pb 0); + \draw[bondc] (pb 0) -- (pc 0); + \draw[bondc] (pc 0) -- (pd 0); + \draw[bondb] (pa 1) -- (pb 1); + \draw[bondc] (pb 1) -- (pc 1); + \draw[bondc] (pc 1) -- (pd 1); + \draw[bondb] (pa 2) -- (pb 2); + \draw[bondc] (pb 2) -- (pc 2); + \draw[bondc] (pc 5) -- (pa 0); + }; + if (\sb==\sbmin) then { + { + \draw (pc 2)[bondc] -- (pd 2); + \draw (pd 2)[bondb] -- (pb 3); + \draw (pb 3)[bondc] -- (pc 3); + }; + }; + if \sa<1 then { + if (\sb==\sbmin || \sa==-\nt then { + { + \draw[bondc] (pc 3) -- (pd 3); + \draw[bondb] (pd 3) -- (pb 4); + \draw[bondc] (pb 4) -- (pc 4); + }; + }; + if (\sb==\sbmax || \sa==-\nt then { + { + \draw[bondc] (pc 4) -- (pd 4); + \draw[bondb] (pd 4) -- (pb 5); + \draw[bondc] (pb 5) -- (pc 5); + }; + }; + }; + { + \draw[fill=red] (oo) circle [radius=1.5pt]; + \draw[fill=red] (pa 0) circle [radius=1.5pt]; + \draw[fill=red] (pa 1) circle [radius=1.5pt]; + \draw[fill=red] (pa 2) circle [radius=1.5pt]; + \draw[fill=red] (pa 3) circle [radius=1.5pt]; + \draw[fill=red] (pa 4) circle [radius=1.5pt]; + \draw[fill=red] (pa 5) circle [radius=1.5pt]; + + \draw[fill=red] (pb 0) circle [radius=1.5pt]; + \draw[fill=red] (pb 1) circle [radius=1.5pt]; + \draw[fill=red] (pb 2) circle [radius=1.5pt]; + \draw[fill=red] (pb 3) circle [radius=1.5pt]; + \draw[fill=red] (pb 4) circle [radius=1.5pt]; + \draw[fill=red] (pb 5) circle [radius=1.5pt]; + + \draw[fill=red] (pc 0) circle [radius=1.5pt]; + \draw[fill=red] (pc 1) circle [radius=1.5pt]; + \draw[fill=red] (pc 2) circle [radius=1.5pt]; + \draw[fill=red] (pc 3) circle [radius=1.5pt]; + \draw[fill=red] (pc 4) circle [radius=1.5pt]; + \draw[fill=red] (pc 5) circle [radius=1.5pt]; + }; + }; + }; + { + \tikzset{ucirc/.style={fill=blue}} + \begin{pgfonlayer}{v2} + % \draw[line width=1pt,-stealth] (oo a0b0) -> (oo a0b1); + % \draw[line width=1pt,-stealth] (oo a0b0) -> (oo a1b0); + % \draw[line width=1pt,dashed,gray] (oo a0b1) -> (oo a1b1); + % \draw[line width=1pt,dashed,gray] (oo a1b0) -> (oo a1b1); + \end{pgfonlayer}{v2} + % \draw[ucirc] (oo a0b0) circle [radius=1.5pt]; + % \draw[ucirc] (pb 0a0b0) circle [radius=1.5pt]; + % \draw[ucirc] (pc 0a0b0) circle [radius=1.5pt]; + % \draw[ucirc] (pd 0a0b0) circle [radius=1.5pt]; + + % \draw[ucirc] (pb 1a0b1) circle [radius=1.5pt]; + % \draw[ucirc] (pc 1a0b1) circle [radius=1.5pt]; + % \draw[ucirc] (pd 1a0b1) circle [radius=1.5pt]; + + % \draw[ucirc] (pa 5a1b0) circle [radius=1.5pt]; + % \draw[ucirc] (pd 5a1b0) circle [radius=1.5pt]; + }; + { + % \node at (3,-1) {$v_1 = \frac{a}{2}\mqty(3\\5\sqrt{3})$}; + % \node at (6,-1) {$v_2 = \frac{a}{2}\mqty(9\\\sqrt{3})$}; + }; + } +\end{tikzpicture} + +\end{document} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: diff --git a/data/docs/source/images/floret_pentagon_structure.pdf b/data/docs/source/images/floret_pentagon_structure.pdf new file mode 100644 index 0000000000000000000000000000000000000000..54e2cef14d0ec336c5fab88a1d0f8ade81139ca3 Binary files /dev/null and b/data/docs/source/images/floret_pentagon_structure.pdf differ diff --git a/data/docs/source/images/floret_pentagon_structure.svg b/data/docs/source/images/floret_pentagon_structure.svg new file mode 100644 index 0000000000000000000000000000000000000000..b2656540af07087b6887619ec833e8a13e4f6fe4 --- /dev/null +++ b/data/docs/source/images/floret_pentagon_structure.svg @@ -0,0 +1,3164 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/data/docs/source/images/floret_pentagon_structure.tex b/data/docs/source/images/floret_pentagon_structure.tex new file mode 100644 index 0000000000000000000000000000000000000000..52330e6a56818dcc043b87704c44f03125f8adcf --- /dev/null +++ b/data/docs/source/images/floret_pentagon_structure.tex @@ -0,0 +1,200 @@ +\documentclass[tikz]{standalone} + +\usepackage{amsfonts} +\usepackage{amsmath} +\usepackage{braket} + +\usepackage{tikz} +\usetikzlibrary{math, calc, decorations, positioning} + +% load TikZ grafic definitions +%\input{gfx_TikZ} + +% main document +\begin{document} + +\pgfdeclarelayer{v1} % background layer +\pgfdeclarelayer{v2} % foreground layer +\pgfsetlayers{v1,main,v2} % set the order of the layers (main is the standard layer) +\tikzset{ + bonda/.style={black}, + bondb/.style={black}, + bondc/.style={black}} +\tikzset{sitenode/.style={fill=red, draw, circle, inner sep=1pt}} +\tikzset{llegs/.style={gray, dashed, thin}} +\tikzset{cggroup/.style={ + draw, dashed, shape=circle, + minimum size=32pt, + line width=.6pt, + fill=black!80!white, + fill opacity=.1,}} + +\tikzset{cgnode/.style={ + draw, shape=circle, + minimum size=12pt, + line width=.6pt, + fill=black, + fill opacity=.6,}} + +\tikzset{middlenode/.style={ + draw, + minimum size=12pt, + line width=.6pt, + fill=red, + fill opacity=.6}} +\begin{tikzpicture} + \tikzmath { + \ang0 = 0; + \lb = 0.5; + \la = 2*\lb; + int \sa; + int \sb; + int \samin; + int \samax; + \samin = -1; + \samax = 1; + function gsbmin(\fsa) { + return max(\samin, \samin-\fsa); + % return -\nt; + % return -1; + }; + function gsbmax(\fsa) { + return min(\samax, \samax-\fsa); + % return \samax; + }; + function ispart(\fa, \fb){ + return (\fa<=\samax && \fa>=\samin && + \fb<=gsbmax(\fa) && \fb>=gsbmin(\fa)); + }; + for \sa in {\samin,...,\samax}{ + int \sbmin, \sbmax; + \sbmin = gsbmin(\sa); + \sbmax = gsbmax(\sa); + for \sb in {\sbmin,...,\sbmax}{ + int \sbp, \sbm, \sap, \sam; + \sbp = \sb + 1; + \sbm = \sb - 1; + \sap = \sa + 1; + \sam = \sa - 1; + coordinate \oo; + \oo = (70.89339464913091+\ang0:9.16515138991168*\sa*\lb/2) + + (10.893394649130906+\ang0:9.16515138991168*\sb*\lb/2); + int \i; + for \i in {0,1,2,3,4,5}{ + \angr = 60*\i+\ang0; + \a1 = 0+\angr; + \a2 = 60+\angr; + \a3 = 120+\angr; + \a4 = 180+\angr; + { + \draw[bonda] (\oo) coordinate (oo) coordinate (oo a\sa b\sb) -- + ++(\a1:\la) coordinate (pa \i) coordinate (pa \i a\sa b\sb) + ++ (\a2:\lb) coordinate (pb \i) coordinate (pb \i a\sa b\sb) + ++ (\a3:\lb) coordinate (pc \i) coordinate (pc \i a\sa b\sb) + ++ (\a4:\lb) coordinate (pd \i) coordinate (pd \i a\sa b\sb); + }; + }; + { + \begin{pgfonlayer}{v1} + \draw[bonda] (pa 0) -- (pb 0) -- (pc 0) -- (pd 0); + \draw[bonda] (pa 1) -- (pb 1) -- (pc 1) -- (pd 1); + \draw[bonda] (pa 2) -- (pb 2) -- (pc 2); + \draw[bonda] (pc 5) -- (pa 0); + \end{pgfonlayer} + }; + if (!ispart(\sa, \sb-1)) then { + { + \draw[bonda] (pc 2) -- (pd 2) -- (pb 3) -- (pc 3); + }; + }; + if (!ispart(\sa-1, \sb)) then { + { + \draw[bonda] (pc 3) -- (pd 3) -- (pb 4) -- (pc 4); + }; + }; + if (!ispart(\sa-1, \sb+1)) then { + { + \draw[bonda] (pc 4) -- (pd 4) -- (pb 5) -- (pc 5); + }; + }; + { + \node[sitenode,name=noo a\sa b\sb] at (oo) {}; + + \node[sitenode,name=npa 0a\sa b\sb] at (pa 0) {}; + \node[sitenode,name=npa 1a\sa b\sb] at (pa 1) {}; + \node[sitenode,name=npa 2a\sa b\sb] at (pa 2) {}; + \node[sitenode,name=npa 3a\sa b\sb] at (pa 3) {}; + \node[sitenode,name=npa 4a\sa b\sb] at (pa 4) {}; + \node[sitenode,name=npa 5a\sa b\sb] at (pa 5) {}; + + \node[sitenode,name=npb 0a\sa b\sb] at (pb 0) {}; + \node[sitenode,name=npb 1a\sa b\sb] at (pb 1) {}; + \node[sitenode,name=npb 2a\sa b\sb] at (pb 2) {}; + \node[sitenode,name=npb 3a\sa b\sb] at (pb 3) {}; + \node[sitenode,name=npb 4a\sa b\sb] at (pb 4) {}; + \node[sitenode,name=npb 5a\sa b\sb] at (pb 5) {}; + + \node[sitenode,name=npc 0a\sa b\sb] at (pc 0) {}; + \node[sitenode,name=npc 1a\sa b\sb] at (pc 1) {}; + \node[sitenode,name=npc 2a\sa b\sb] at (pc 2) {}; + \node[sitenode,name=npc 3a\sa b\sb] at (pc 3) {}; + \node[sitenode,name=npc 4a\sa b\sb] at (pc 4) {}; + \node[sitenode,name=npc 5a\sa b\sb] at (pc 5) {}; + }; + }; + }; + for \sa in {\samin,...,\samax}{ + int \sbmin, \sbmax; + \sbmin = gsbmin(\sa); + \sbmax = gsbmax(\sa); + for \sb in {\sbmin,...,\sbmax}{ + int \sbp, \sbm, \sap, \sam; + \sbp = \sb + 1; + \sbm = \sb - 1; + \sap = \sa + 1; + \sam = \sa - 1; + int \i; + for \i in {0,1,2,3,4,5}{ + \angr = 60*\i+\ang0; + \a1 = 0+\angr; + \a2 = 60+\angr; + \a3 = 120+\angr; + \a4 = 180+\angr; + { + \path (oo a\sa b\sb) coordinate (oo) + ++(\a1:\la) coordinate (pa \i) coordinate (pa \i a\sa b\sb) + ++ (\a2:\lb) coordinate (pb \i) coordinate (pb \i a\sa b\sb) + ++ (\a3:\lb) coordinate (pc \i) coordinate (pc \i a\sa b\sb) + ++ (\a4:\lb) coordinate (pd \i) coordinate (pd \i a\sa b\sb); + }; + }; + }; + }; + { + \tikzset{ucirc/.style={sitenode, fill=blue}}; + \begin{pgfonlayer}{v2} + \draw[line width=1pt,dashed,gray] (oo a0b1) -> (oo a-1b1); + \draw[line width=1pt,dashed,gray] (oo a-1b0) -> (oo a-1b1); + \draw[line width=.75pt,-stealth] (oo a0b0) -> (oo a0b1) node[midway, label=110:$v_2$] {}; + \draw[line width=.75pt,-stealth] (oo a0b0) -> (oo a-1b0) node[midway, label=110:$v_1$] {}; + + \node[ucirc, label={\small 1}] at (oo a0b0) {}; + \node[ucirc, label=200:{\small 2}] at (pa 0a0b0) {}; + \node[ucirc, label={\small 3}] at (pa 5a0b0) {}; + \node[ucirc, label={\small 4}] at (pc 5a0b0) {}; + \node[ucirc, label={\small 6}] at (pb 5a0b0) {}; + \node[ucirc, label={\small 5}] at (pa 4a0b1) {}; + \node[ucirc, label={\small 7}] at (pc 4a0b0) {}; + \node[ucirc, label={\small 9}] at (pb 4a0b0) {}; + \node[ucirc, label={\small 8}] at (pb 0a-1b0) {}; + \end{pgfonlayer}{v2} + }; + } +\end{tikzpicture} + +\end{document} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: diff --git a/data/docs/source/images/honeycomb_structure.pdf b/data/docs/source/images/honeycomb_structure.pdf new file mode 100644 index 0000000000000000000000000000000000000000..c2dbcb0fc49c07b7c8a8a5db416a9e9d650c1447 Binary files /dev/null and b/data/docs/source/images/honeycomb_structure.pdf differ diff --git a/data/docs/source/images/honeycomb_structure.svg b/data/docs/source/images/honeycomb_structure.svg new file mode 100644 index 0000000000000000000000000000000000000000..47fa2686f0f2a0bffe7a1015b33a41b1cd63324f --- /dev/null +++ b/data/docs/source/images/honeycomb_structure.svg @@ -0,0 +1,1136 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/data/docs/source/images/honeycomb_structure.tex b/data/docs/source/images/honeycomb_structure.tex new file mode 100644 index 0000000000000000000000000000000000000000..80b0675b1e8f05c959a24116ee71b8c2af25fd84 --- /dev/null +++ b/data/docs/source/images/honeycomb_structure.tex @@ -0,0 +1,159 @@ +\documentclass[tikz]{standalone} + +\usepackage{amsfonts} +\usepackage{amsmath} +\usepackage{braket} + +\usepackage{tikz} +\usetikzlibrary{shapes.geometric,patterns,positioning,matrix} +\usetikzlibrary{shadows,calc,3d,arrows.meta,decorations.pathmorphing,decorations.markings,decorations.pathreplacing} + +\definecolor{googleB}{HTML}{4285F4} +\definecolor{googleG}{HTML}{34A853} +\definecolor{googleY}{HTML}{FBBC05} +\definecolor{googleR}{HTML}{EA4335} +\definecolor{googleBG}{HTML}{3B96A4} + +% load TikZ grafic definitions +%\input{gfx_TikZ} + +% main document +\begin{document} + \begin{tikzpicture} + + \def\colorX{googleG} + \def\colorY{googleR} + \def\colorZ{googleB} + + \begin{scope}[shift = {(+1.5, +1.5)}] + \foreach \x in {-2, +2} { + \draw[thick, \colorZ, shift = {(\x, 0)}, rotate = 45] (-{sqrt(2)/2 - 0.15}, 0) to (0, 0); + \draw[thick, \colorZ, shift = {(\x, 0)}, rotate = 45, dotted] (0, 0) to (+{sqrt(2)/4}, 0); + } + % \foreach \x in {-4, 0, +4} { + % \draw[thick, gray, shift = {(\x, 0)}, rotate = 45, dotted] (-{sqrt(2)/2 - 0.15}, 0) to (+{sqrt(2)/4}, 0); + % } + \end{scope} + + \begin{scope}[shift = {(+1, +1)}] + \begin{scope}[shift = {(-4, 0)}] + \draw[thick, \colorY, dotted] (-1.0, 0) to (-0.5, 0); + \draw[thick, \colorY] (-0.5, 0) to (-0.0, 0); + \end{scope} + \foreach \x in {-3, +1} { + \draw[thick, \colorX, shift = {(\x, 0)}] (-0.85, 0) to (+0.85, 0); + \draw[thick, gray, dotted, shift = {(\x, 0)}] (-1.75, -0.25) to (+1.25, -0.25) to (+1.75, +0.25) to (-1.25, +0.25) -- cycle; + } + \foreach \x in {-1, +3} { + \draw[thick, \colorY, shift = {(\x, 0)}] (-0.85, 0) to (+0.85, 0); + } + \begin{scope}[shift = {(+4, 0)}] + \draw[thick, \colorX] (+0.0, 0) to (+0.5, 0); + \draw[thick, \colorX, dotted] (+0.5, 0) to (+1.0, 0); + \end{scope} + + \foreach \x in {-4, 0, +4} { + \draw[thick] (\x,0) to (\x, -0.5); + \draw[thick, black, fill = white] (\x, 0) circle (0.15); + } + \foreach \x in {-2, +2} { + \draw[thick] (\x,0) to (\x, -0.5); + \draw[thick, black, fill = black] (\x, 0) circle (0.15); + } + \end{scope} + + \begin{scope}[shift = {(+0.5, +0.5)}] + \foreach \x in {-4, 0, +4} { + \draw[thick, \colorZ, shift = {(\x, 0)}, rotate = 45] (-{sqrt(2)/2 - 0.15}, 0) to (+{sqrt(2)/2 - 0.15}, 0); + } + % \foreach \x in {-2, +2} { + % \draw[thick, gray, shift = {(\x, 0)}, rotate = 45, dotted] (-{sqrt(2)/2 - 0.15}, 0) to (+{sqrt(2)/2 - 0.15}, 0); + % } + \end{scope} + + \begin{scope}[shift = {(0, 0)}] + \begin{scope}[shift = {(-4, 0)}] + \draw[thick, \colorX, dotted] (-1.0, 0) to (-0.5, 0); + \draw[thick, \colorX] (-0.5, 0) to (-0.0, 0); + \end{scope} + \foreach \x in {-1, +3} { + \draw[thick, \colorX, shift = {(\x, 0)}] (-0.85, 0) to (+0.85, 0); + \draw[thick, gray, dotted, shift = {(\x, 0)}] (-1.75, -0.25) to (+1.25, -0.25) to (+1.75, +0.25) to (-1.25, +0.25) -- cycle; + } + \foreach \x in {-3, +1} { + \draw[thick, \colorY, shift = {(\x, 0)}] (-0.85, 0) to (+0.85, 0); + } + \begin{scope}[shift = {(+4, 0)}] + \draw[thick, \colorY] (+0.0, 0) to (+0.5, 0); + \draw[thick, \colorY, dotted] (+0.5, 0) to (+1.0, 0); + \end{scope} + + \foreach \x in {-2, +2} { + \draw[thick] (\x,0) to (\x, -0.5); + \draw[thick, black, fill = white] (\x, 0) circle (0.15); + } + \foreach \x in {-4, 0, +4} { + \draw[thick] (\x,0) to (\x, -0.5); + \draw[thick, black, fill = black] (\x, 0) circle (0.15); + } + \end{scope} + + \begin{scope}[shift = {(-0.5, -0.5)}] + \foreach \x in {-2, +2} { + \draw[thick, \colorZ, shift = {(\x, 0)}, rotate = 45] (-{sqrt(2)/2 - 0.15}, 0) to (+{sqrt(2)/2 - 0.15}, 0); + } + % \foreach \x in {-4, 0, +4} { + % \draw[thick, gray, shift = {(\x, 0)}, rotate = 45, dotted] (-{sqrt(2)/2 - 0.15}, 0) to (+{sqrt(2)/2 - 0.15}, 0); + % } + \end{scope} + + \begin{scope}[shift = {(-1, -1)}] + \begin{scope}[shift = {(-4, 0)}] + \draw[thick, \colorY, dotted] (-1.0, 0) to (-0.5, 0); + \draw[thick, \colorY] (-0.5, 0) to (-0.0, 0); + \end{scope} + \foreach \x in {-3, +1} { + \draw[thick, \colorX, shift = {(\x, 0)}] (-0.85, 0) to (+0.85, 0); + \draw[thick, gray, dotted, shift = {(\x, 0)}] (-1.75, -0.25) to (+1.25, -0.25) to (+1.75, +0.25) to (-1.25, +0.25) -- cycle; + } + \foreach \x in {-1, +3} { + \draw[thick, \colorY, shift = {(\x, 0)}] (-1.0, 0) to (+1.0, 0); + } + \begin{scope}[shift = {(+4, 0)}] + \draw[thick, \colorX] (+0.0, 0) to (+0.5, 0); + \draw[thick, \colorX, dotted] (+0.5, 0) to (+1.0, 0); + \end{scope} + + \foreach \x in {-4, 0, +4} { + \draw[thick] (\x,0) to (\x, -0.5); + \draw[thick, black, fill = white] (\x, 0) circle (0.15); + } + \foreach \x in {-2, +2} { + \draw[thick] (\x,0) to (\x, -0.5); + \draw[thick, black, fill = black] (\x, 0) circle (0.15); + } + \end{scope} + + \begin{scope}[shift = {(-1.5, -1.5)}] + \foreach \x in {-4, 0, +4} { + \draw[thick, \colorZ, shift = {(\x, 0)}, rotate = 45] (0, 0) to (+{sqrt(2)/2 - 0.15}, 0); + \draw[thick, \colorZ, shift = {(\x, 0)}, rotate = 45, dotted] (0, 0) to (-{sqrt(2)/4}, 0); + } + % \foreach \x in {-2, +2} { + % \draw[thick, gray, shift = {(\x, 0)}, rotate = 45, dotted] (-{sqrt(2)/4}, 0) to (+{sqrt(2)/2 - 0.15}, 0); + % } + \end{scope} + + \node at (+7.0, +0.5) {{\color{\colorX}$x$}-link}; + \node at (+6.5, +0.0) {{\color{\colorY}$y$}-link}; + \node at (+6.0, -0.5) {{\color{\colorZ}$z$}-link}; + + + \end{tikzpicture} + +\end{document} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: diff --git a/data/docs/source/images/kagome_structure.pdf b/data/docs/source/images/kagome_structure.pdf new file mode 100644 index 0000000000000000000000000000000000000000..0867a72b680746c1ebdec5f261ba1201a285f083 Binary files /dev/null and b/data/docs/source/images/kagome_structure.pdf differ diff --git a/data/docs/source/images/kagome_structure.svg b/data/docs/source/images/kagome_structure.svg new file mode 100644 index 0000000000000000000000000000000000000000..20a5f010c1f3d64957853b92c33f9c10d52c9443 --- /dev/null +++ b/data/docs/source/images/kagome_structure.svg @@ -0,0 +1,926 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/data/docs/source/images/kagome_structure.tex b/data/docs/source/images/kagome_structure.tex new file mode 100644 index 0000000000000000000000000000000000000000..1dfe7434d1dbf7feff131326bfccf5b2ea3c37dd --- /dev/null +++ b/data/docs/source/images/kagome_structure.tex @@ -0,0 +1,104 @@ +\documentclass[tikz]{standalone} + +\usepackage{amsfonts} +\usepackage{amsmath} +\usepackage{braket} + +\usepackage{tikz} +\usetikzlibrary{shapes.geometric,patterns,positioning,matrix} +\usetikzlibrary{shadows,calc,3d,arrows.meta,decorations.pathmorphing,decorations.markings,decorations.pathreplacing} + +\definecolor{googleB}{HTML}{4285F4} +\definecolor{googleG}{HTML}{34A853} +\definecolor{googleY}{HTML}{FBBC05} +\definecolor{googleR}{HTML}{EA4335} +\definecolor{googleBG}{HTML}{3B96A4} + +% load TikZ grafic definitions +%\input{gfx_TikZ} + +% main document +\begin{document} + + \begin{tikzpicture} + + \def\disT{0.750} + \def\tensorSize{0.125} + + % \begin{scope}[shift = {(-4.5, +3.25)}] + % \draw[thick, -{Stealth[scale = 1.0]}] (0 : 0) to (240 : 1.0) node at (240 : 1.25) {$x$}; + % \draw[thick, -{Stealth[scale = 1.0]}] (0 : 0) to ( 0 : 1.0) node at ( 0 : 1.25) {$y$}; + % \end{scope} + + \foreach \x in {-6, -2, +2} { + + \foreach \y in {0} { + + \begin{scope}[shift = {({\x*\disT*cos(30)}, \y*\disT)}] + + \coordinate (T1) at (210 : \disT); + \coordinate (T2) at ( 90 : \disT); + \coordinate (T3) at (330 : \disT); + + % draw inter-layer T1-T2-T3 + \draw[thick] (T1) to (T2) to (T3) -- cycle; + \draw[thick] (T1) to ($(T1) + (180 : {1.0 * cos(30) * \disT})$); + \draw[thick] (T1) to ($(T1) + (240 : {1.0 * cos(30) * \disT})$); + \draw[thick] (T2) to ($(T2) + ( 60 : {1.0 * cos(30) * \disT})$); + \draw[thick] (T2) to ($(T2) + (120 : {1.0 * cos(30) * \disT})$); + \draw[thick] (T3) to ($(T3) + ( 0 : {1.0 * cos(30) * \disT})$); + \draw[thick] (T3) to ($(T3) + (300 : {1.0 * cos(30) * \disT})$); + + \foreach \T in {T1, T2, T3} { + \draw[thick, fill = white] (\T) circle (\tensorSize); + } + + % draw unit cell borders + \draw[thick, gray, dotted, rounded corners] ($(T2) + (90 : 0.50)$) to ($(T1) + (210 : 0.50)$) to ($(T3) + (330 : 0.50)$) -- cycle; + + \end{scope} + + } + + } + + \foreach \x in {-4, 0, +4} { + + \foreach \y in {+4.0} { + + \begin{scope}[shift = {({\x*\disT*cos(30)}, {\y*\disT*cos(30)*tan(60)/2})}] + + \coordinate (T1) at (210 : \disT); + \coordinate (T2) at ( 90 : \disT); + \coordinate (T3) at (330 : \disT); + + % draw inter-layer T1-T2-T3 + \draw[thick] (T1) to (T2) to (T3) -- cycle; + \draw[thick] (T1) to ($(T1) + (180 : {1.0 * cos(30) * \disT})$); + \draw[thick] (T1) to ($(T1) + (240 : {1.0 * cos(30) * \disT})$); + \draw[thick] (T2) to ($(T2) + ( 60 : {1.0 * cos(30) * \disT})$); + \draw[thick] (T2) to ($(T2) + (120 : {1.0 * cos(30) * \disT})$); + \draw[thick] (T3) to ($(T3) + ( 0 : {1.0 * cos(30) * \disT})$); + \draw[thick] (T3) to ($(T3) + (300 : {1.0 * cos(30) * \disT})$); + + \foreach \T in {T1, T2, T3} { + \draw[thick, fill = white] (\T) circle (\tensorSize); + } + + % draw unit cell borders + \draw[thick, gray, dotted, rounded corners] ($(T2) + (90 : 0.50)$) to ($(T1) + (210 : 0.50)$) to ($(T3) + (330 : 0.50)$) -- cycle; + + \end{scope} + + } + + } + + \end{tikzpicture} + +\end{document} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: diff --git a/data/docs/source/images/logo.pdf b/data/docs/source/images/logo.pdf new file mode 100644 index 0000000000000000000000000000000000000000..d452c3b35b74b734ee3b3ee8fc3df1257997e522 Binary files /dev/null and b/data/docs/source/images/logo.pdf differ diff --git a/data/docs/source/images/logo.png b/data/docs/source/images/logo.png new file mode 100644 index 0000000000000000000000000000000000000000..e915d39d6837d70f8dd639cf675860d45df66750 --- /dev/null +++ b/data/docs/source/images/logo.png @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:1700ac6ed28e1fe18413742324b66fb623728ec7a193f371c4a5922f881187f9 +size 43277 diff --git a/data/docs/source/images/logo.svg b/data/docs/source/images/logo.svg new file mode 100644 index 0000000000000000000000000000000000000000..6dbcb5a8dba33ddb6aa06c2213279a42e6e38788 --- /dev/null +++ b/data/docs/source/images/logo.svg @@ -0,0 +1,800 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/data/docs/source/images/logo.tex b/data/docs/source/images/logo.tex new file mode 100644 index 0000000000000000000000000000000000000000..49db1b30b47b3887212d3ca4fabe0d6cb38928aa --- /dev/null +++ b/data/docs/source/images/logo.tex @@ -0,0 +1,100 @@ +\documentclass[tikz]{standalone} + +\usepackage{lmodern} +\usepackage{microtype} +\usepackage{amsfonts} +\usepackage{amsmath} +\usepackage{braket} + +\usepackage{tikz} +\usetikzlibrary{calc, decorations, positioning} + +\pagecolor{white} + +\definecolor{googleB}{HTML}{4285F4} +\definecolor{googleG}{HTML}{34A853} +\definecolor{googleY}{HTML}{FBBC05} +\definecolor{googleR}{HTML}{EA4335} +\definecolor{googleBG}{HTML}{3B96A4} + +% Main Document +\begin{document} +\begin{tikzpicture} + \def\clipX{2.00} + \def\clipY{1.75} + \def\legLength{0.175} + \def\tensorSize{0.15} + \def\tensorShiftY{0.25} + + % ------------------------ + % triangular lattice sites + % ------------------------ + + \node at (3.15, 0.4\baselineskip) {\Huge\sffamily {\color{googleY}vari}{\color{googleB}PEPS}}; + \node at (3.15, -1.15\baselineskip) {\upshape Variational PEPS Library}; + + % define coordinates for the triangular lattice + \coordinate (T1) at ({+0.0*cos(30)}, {+0.0*cos(30)*tan(60)/2}); + + \coordinate (C1) at ($(T1) + ({-0.5*cos(30)}, {+1.0*cos(30)*tan(60)/2})$); + \coordinate (C2) at ($(T1) + ({+0.5*cos(30)}, {+1.0*cos(30)*tan(60)/2})$); + \coordinate (C3) at ($(T1) + ({+1.0*cos(30)}, 0)$); + \coordinate (C4) at ($(T1) + ({+0.5*cos(30)}, {-1.0*cos(30)*tan(60)/2})$);; + \coordinate (C5) at ($(T1) + ({-0.5*cos(30)}, {-1.0*cos(30)*tan(60)/2})$); + \coordinate (C6) at ($(T1) + ({-1.0*cos(30)}, 0)$); + + \draw[very thick] (C1) to (C2); + \draw[very thick] (C2) to (C3); + \draw[very thick] (C3) to (C4); + \draw[very thick] (C4) to (C5); + \draw[very thick] (C5) to (C6); + \draw[very thick] (C6) to (C1); + + \draw[thick] ($(T1) + (0, +\tensorShiftY)$) to (C1); + \draw[thick] ($(T1) + (0, -\tensorShiftY)$) to (C1); + \draw[thick] ($(T1) + (0, +\tensorShiftY)$) to (C2); + \draw[thick] ($(T1) + (0, -\tensorShiftY)$) to (C2); + \draw[thick] ($(T1) + (0, +\tensorShiftY)$) to (C3); + \draw[thick] ($(T1) + (0, -\tensorShiftY)$) to (C3); + \draw[thick] ($(T1) + (0, +\tensorShiftY)$) to (C4); + \draw[thick] ($(T1) + (0, -\tensorShiftY)$) to (C4); + \draw[thick] ($(T1) + (0, +\tensorShiftY)$) to (C5); + \draw[thick] ($(T1) + (0, -\tensorShiftY)$) to (C5); + \draw[thick] ($(T1) + (0, +\tensorShiftY)$) to (C6); + \draw[thick] ($(T1) + (0, -\tensorShiftY)$) to (C6); + + \begin{scope}[shift = {(T1)}] + \begin{scope}[shift = {(0, +\tensorShiftY)}] + % \draw[thick] (0,0) to ({-0.5*cos(30)}, {-1.0*cos(30)*tan(60)/2}); + % \draw[thick] ({+0.5*cos(30)}, {+1.0*cos(30)*tan(60)/2}) to (0, 0); + % \draw[thick] ({-0.5*cos(30)}, {+1.0*cos(30)*tan(60)/2}) to (0, 0); + % \draw[thick] (0, 0) to ({+0.5*cos(30)}, {-1.0*cos(30)*tan(60)/2}); + % \draw[thick] (0, 0) to ({-1.0*cos(30)}, 0); + % \draw[thick] ({+1.0*cos(30)}, 0) to (0, 0); + \draw[thick] (0, 0) to (0, -\tensorShiftY); + \draw[black, fill = googleB] (0, 0) circle (\tensorSize); + \end{scope} + \begin{scope}[shift = {(0, -\tensorShiftY)}] + % \draw[thick] (0,0) to ({-0.5*cos(30)}, {-1.0*cos(30)*tan(60)/2}); + % \draw[thick] ({+0.5*cos(30)}, {+1.0*cos(30)*tan(60)/2}) to (0, 0); + % \draw[thick] ({-0.5*cos(30)}, {+1.0*cos(30)*tan(60)/2}) to (0, 0); + % \draw[thick] (0, 0) to ({+0.5*cos(30)}, {-1.0*cos(30)*tan(60)/2}); + % \draw[thick] (0, 0) to ({-1.0*cos(30)}, 0); + % \draw[thick] ({+1.0*cos(30)}, 0) to (0, 0); + \draw[thick] (0, 0) to (0, +\tensorShiftY); + \draw[black, fill = googleB] (0, 0) circle (\tensorSize); + \end{scope} + \end{scope} + + \foreach \tensor in {C1, C2, C3, C4, C5, C6} { + \begin{scope}[shift = {(\tensor)}] + \draw[black, fill = gray] (0, 0) circle (\tensorSize); + \end{scope} + } +\end{tikzpicture} +\end{document} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: diff --git a/data/docs/source/images/maple_leaf_structure.pdf b/data/docs/source/images/maple_leaf_structure.pdf new file mode 100644 index 0000000000000000000000000000000000000000..e8910c90f27ae9fb973bfa04040e0927308dd790 Binary files /dev/null and b/data/docs/source/images/maple_leaf_structure.pdf differ diff --git a/data/docs/source/images/maple_leaf_structure.svg b/data/docs/source/images/maple_leaf_structure.svg new file mode 100644 index 0000000000000000000000000000000000000000..9ffb7c975e8886d21b78011e8cce9e42576f6419 --- /dev/null +++ b/data/docs/source/images/maple_leaf_structure.svg @@ -0,0 +1,3099 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/data/docs/source/images/maple_leaf_structure.tex b/data/docs/source/images/maple_leaf_structure.tex new file mode 100644 index 0000000000000000000000000000000000000000..5a14b3fe0f97b7ed2c4b37beae5c96c28d432451 --- /dev/null +++ b/data/docs/source/images/maple_leaf_structure.tex @@ -0,0 +1,100 @@ +\documentclass[tikz]{standalone} + +\usepackage{amsfonts} +\usepackage{amsmath} +\usepackage{braket} + +\usepackage{tikz} +\usetikzlibrary{shapes.geometric,patterns,positioning,matrix} +\usetikzlibrary{shadows,calc,3d,arrows.meta,decorations.pathmorphing,decorations.markings,decorations.pathreplacing} + +\definecolor{googleB}{HTML}{4285F4} +\definecolor{googleG}{HTML}{34A853} +\definecolor{googleY}{HTML}{FBBC05} +\definecolor{googleR}{HTML}{EA4335} +\definecolor{googleBG}{HTML}{3B96A4} + +% load TikZ grafic definitions +%\input{gfx_TikZ} + +% main document +\begin{document} + + \begin{tikzpicture} + + \def\clipX{2.00} + \def\clipY{1.75} + \def\legLength{0.85} + \def\tensorSize{0.1} + \def\alpha{19.1066} + + % lattice vectors + \begin{scope}[shift = {(0, 0)}] + \draw[thick, -{Stealth[scale = 1.0]}] (0, 0) to ({-1*cos(30)*\legLength*sin(30)/sin(\alpha)}, {-2*cos(30)*tan(60)/2*\legLength*sin(30)/sin(\alpha)}) node at ($(240 : 1.25) + (150 : 0.25)$) {$\boldsymbol{a}_1$}; + \draw[thick, -{Stealth[scale = 1.0]}] (0, 0) to ({+2*cos(30)*\legLength*sin(30)/sin(\alpha)}, {+0*cos(30)*tan(60)/2*\legLength*sin(30)/sin(\alpha)}) node at ($( 0 : 1.00) + ( 90 : 0.25)$) {$\boldsymbol{a}_2$}; + \end{scope} + + % maple-leaf unit cells + \begin{scope}[shift = {(0, 0)}] + + \foreach \x/\y in {0/0, 2/0, 4/0, -1/-2, +1/-2, +3/-2} { + + \begin{scope}[shift = {({\x*cos(30)*\legLength*sin(30)/sin(\alpha)}, {\y*cos(30)*tan(60)/2*\legLength*sin(30)/sin(\alpha)}, 0)}] + + \coordinate (1) at (0, 0); + \coordinate (2) at ({-\alpha - 60} : {1*\legLength}); + \coordinate (3) at ({-\alpha - 60} : {2*\legLength}); + \coordinate (4) at ($(2) + ({-\alpha} : \legLength)$); + \coordinate (5) at ($(1) + ({-\alpha} : \legLength)$); + \coordinate (6) at ({-\alpha} : {2*\legLength}); + + % internal links + \draw[ultra thick, googleG] (1) to (2); + \draw[ultra thick, googleG] (3) to (4); + \draw[ultra thick, googleG] (5) to (6); + \draw[thick, googleB, densely dashed] (1) to (5); + \draw[thick, googleB, densely dashed] (2) to (3); + \draw[thick, googleB, densely dashed] (4) to (6); + \draw[thick, googleR, densely dotted] (2) to (5) to (4) to (2); + + % external links + \draw[thick, googleB, densely dashed] (1) to ($(1) + ({120 - \alpha} : 0.5 * \legLength)$); + \draw[thick, googleR, densely dotted] (1) to ($(1) + ({180 - \alpha} : 0.5 * \legLength)$); + \draw[thick, googleR, densely dotted] (1) to ($(1) + ({240 - \alpha} : 0.5 * \legLength)$); + + \draw[thick, googleB, densely dashed] (2) to ($(2) + ({180 - \alpha} : 0.5 * \legLength)$); + + \draw[thick, googleB, densely dashed] (3) to ($(3) + ({240 - \alpha} : 0.5 * \legLength)$); + \draw[thick, googleR, densely dotted] (3) to ($(3) + ({300 - \alpha} : 0.5 * \legLength)$); + \draw[thick, googleR, densely dotted] (3) to ($(3) + ({360 - \alpha} : 0.5 * \legLength)$); + + \draw[thick, googleB, densely dashed] (4) to ($(4) + ({300 - \alpha} : 0.5 * \legLength)$); + + \draw[thick, googleB, densely dashed] (5) to ($(5) + ({ 60 - \alpha} : 0.5 * \legLength)$); + + \draw[thick, googleB, densely dashed] (6) to ($(6) + ({360 - \alpha} : 0.5 * \legLength)$); + \draw[thick, googleR, densely dotted] (6) to ($(6) + ({ 60 - \alpha} : 0.5 * \legLength)$); + \draw[thick, googleR, densely dotted] (6) to ($(6) + ({120 - \alpha} : 0.5 * \legLength)$); + + % lattice site + \foreach \siteIdx in {1, 2, 3, 4, 5, 6} { + \draw[black, fill = black] (\siteIdx) circle (\tensorSize); + \draw[black, fill = black] (\siteIdx) circle (\tensorSize) node[white] at (\siteIdx) {\tiny$\siteIdx$}; + } + + \draw[thick, gray, dotted, rounded corners] ($(1) + ({150 - \alpha} : 0.5 * \legLength)$) to ($(3) + ({270 - \alpha} : 0.5 * \legLength)$) to ($(6) + ({ 30 - \alpha} : 0.5 * \legLength)$) -- cycle; + + \end{scope} + + } + + \end{scope} + + \end{tikzpicture} + +\end{document} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: diff --git a/data/docs/source/images/square_kagome_structure.pdf b/data/docs/source/images/square_kagome_structure.pdf new file mode 100644 index 0000000000000000000000000000000000000000..f6bb56a566d4f068e58ebf585206d3fd3b15c549 Binary files /dev/null and b/data/docs/source/images/square_kagome_structure.pdf differ diff --git a/data/docs/source/images/square_kagome_structure.svg b/data/docs/source/images/square_kagome_structure.svg new file mode 100644 index 0000000000000000000000000000000000000000..c691bad69ca43a21f0f36fed7400f60bf6953f0f --- /dev/null +++ b/data/docs/source/images/square_kagome_structure.svg @@ -0,0 +1,2323 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/data/docs/source/images/square_kagome_structure.tex b/data/docs/source/images/square_kagome_structure.tex new file mode 100644 index 0000000000000000000000000000000000000000..604f67fecdc0469905ae641f91f63190dd77d11c --- /dev/null +++ b/data/docs/source/images/square_kagome_structure.tex @@ -0,0 +1,109 @@ +\documentclass[tikz]{standalone} + +\usepackage{amsfonts} +\usepackage{amsmath} +\usepackage{braket} + +\usepackage{tikz} +\usetikzlibrary{shapes.geometric,patterns,positioning,matrix} +\usetikzlibrary{shadows,calc,3d,arrows.meta,decorations.pathmorphing,decorations.markings,decorations.pathreplacing} + +\definecolor{googleB}{HTML}{4285F4} +\definecolor{googleG}{HTML}{34A853} +\definecolor{googleY}{HTML}{FBBC05} +\definecolor{googleR}{HTML}{EA4335} +\definecolor{googleBG}{HTML}{3B96A4} + +% load TikZ grafic definitions +%\input{gfx_TikZ} + +% main document +\begin{document} + + \begin{tikzpicture} + + \def\disL{0.75} + \def\tensorSizeL{0.125} + \def\tensorSizeS{0.150} + + \begin{scope}[shift = {(-0.5, +0.5)}] + \draw[thick, -{Stealth[scale = 1.0]}] (0, 0) to (0, -1.25) node at (0, -1.50) {$x$}; + \draw[thick, -{Stealth[scale = 1.0]}] (0, 0) to (+1.25, 0) node at (+1.50, 0) {$y$}; + \end{scope} + + \foreach \x in {-1, +1, +3} { + + \foreach \y in {-1, +1} { + + \begin{scope}[shift = {({\x * \disL + \x * tan(60) * \disL}, {\y * \disL + \y * tan(60) * \disL})}] + + % define Square-Kagome lattice coordiates + % \coordinate (1) at ($(0, {-\disL - tan(30) * \disL}) + (270 : {\disL / cos(30)})$); + \coordinate (1) at (0, {- \disL - \disL / tan(30)}); + \coordinate (2) at (-\disL, -\disL); + \coordinate (3) at (-\disL, +\disL); + \coordinate (4) at (+\disL, -\disL); + \coordinate (5) at (+\disL, +\disL); + % \coordinate (6) at ($({+\disL + tan(30) * \disL}, 0) + ( 0 : {\disL / cos(30)})$); + \coordinate (6) at ({+\disL + \disL / tan(30)}, 0); + + % define iPESS coordinates + \coordinate (SL) at ({-\disL - tan(30) * \disL}, 0); + \coordinate (SU) at (0, {+\disL + tan(30) * \disL}); + \coordinate (SR) at ({+\disL + tan(30) * \disL}, 0); + \coordinate (SD) at (0, {-\disL - tan(30) * \disL}); + + % Square-Kagome lattice links + \draw[gray] (2) to (3) to (5) to (4) -- cycle; + + \draw[gray] (1) to ($(1) + ( 60 : \disL)$); + \draw[gray] (1) to ($(1) + (120 : \disL)$); + \draw[gray] (1) to ($(1) + (240 : \disL)$); + \draw[gray] (1) to ($(1) + (300 : \disL)$); + + \draw[gray] (2) to ($(2) + (150 : \disL)$); + \draw[gray] (2) to ($(2) + (300 : \disL)$); + + \draw[gray] (3) to ($(3) + ( 60 : \disL)$); + \draw[gray] (3) to ($(3) + (210 : \disL)$); + + \draw[gray] (4) to ($(4) + (240 : \disL)$); + \draw[gray] (4) to ($(4) + ( 30 : \disL)$); + + \draw[gray] (5) to ($(5) + (330 : \disL)$); + \draw[gray] (5) to ($(5) + (120 : \disL)$); + + \draw[gray] (6) to ($(6) + ( 30 : \disL)$); + \draw[gray] (6) to ($(6) + (150 : \disL)$); + \draw[gray] (6) to ($(6) + (210 : \disL)$); + \draw[gray] (6) to ($(6) + (330 : \disL)$); + + % Square-Kagome lattice sites + \foreach \site in {1, 2, 3, 4, 5, 6} { + \draw[thick, fill = white] (\site) circle (\tensorSizeL); + } + + % draw coarse-grained tensor + \draw[thick] (0, 0) to ($(-\disL, 0) + 0.5*(150 : {\disL}) + 0.5*(210 : {\disL})$); + \draw[thick] (0, 0) to ($(0, +\disL) + 0.5*(60 : {\disL}) + 0.5*(120 : {\disL})$); + \draw[thick] (0, 0) to ($(0, {- \disL - \disL / tan(30)}) + 0.5*(240 : {\disL}) + 0.5*(300 : {\disL})$); + \draw[thick] (0, 0) to ($({+ \disL + \disL / tan(30)}, 0) + 0.5*(30 : {\disL}) + 0.5*(330 : {\disL})$); + \draw[thick, fill = googleB] (0, 0) circle (\tensorSizeS); + + + % draw unit cell borders + \draw[gray, very thick, dotted] ($(3) + (135 : 0.30)$) to ($(5) + ( 45 : 0.30)$) to ($(6) + ( 30 : 0.30)$) to ($(6) + (330 : 0.30)$) to ($(4) + (315 : 0.30)$) to ($(1) + (300 : 0.30)$) to ($(1) + (240 : 0.30)$) to ($(2) + (225 : 0.30)$) -- cycle; + + \end{scope} + } + + } + + \end{tikzpicture} + +\end{document} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: diff --git a/data/docs/source/images/square_lattice.pdf b/data/docs/source/images/square_lattice.pdf new file mode 100644 index 0000000000000000000000000000000000000000..52f2b82eb2609a0c72782c571b83ad5b83113808 Binary files /dev/null and b/data/docs/source/images/square_lattice.pdf differ diff --git a/data/docs/source/images/square_lattice.svg b/data/docs/source/images/square_lattice.svg new file mode 100644 index 0000000000000000000000000000000000000000..b29cd2768ffc18948fadfdfa3b69f7384fec4104 --- /dev/null +++ b/data/docs/source/images/square_lattice.svg @@ -0,0 +1,548 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/data/docs/source/images/square_lattice.tex b/data/docs/source/images/square_lattice.tex new file mode 100644 index 0000000000000000000000000000000000000000..9cdab86733e510ac05d3358c6b946d58e1a994ed --- /dev/null +++ b/data/docs/source/images/square_lattice.tex @@ -0,0 +1,36 @@ +\documentclass[tikz]{standalone} + +\usepackage{amsfonts} +\usepackage{amsmath} +\usepackage{braket} + +\usepackage{tikz} +\usetikzlibrary{calc, decorations, positioning} + +\definecolor{googleR}{HTML}{DB4437} +\definecolor{googleG}{HTML}{0F9D58} +\definecolor{googleB}{HTML}{4285F4} + +% main document +\begin{document} + \begin{tikzpicture}[] + \foreach \y in {-0.75, -0.25, +0.25} { + \foreach \x in {-1.5, -0.5, +0.5, +1.5} { + \begin{scope}[shift = {(2*\x + 2*\y, 2*\y)}] + \draw[thick, googleR] (-1.00, 0) to (-0.00, 0); + \draw[thick, googleR] (+0.00, 0) to (+1.00, 0); + \draw[thick, googleB] (-0.50, -0.50) to (0, 0); + \draw[thick, googleB] (0, 0) to (+0.50, +0.50); + \draw[thick] (0, 0) to (0, -0.50); + \draw[thick, fill = googleG] (0,0) circle (0.15); + % \draw[thick, googleG] (-0.15, 0) to (+0.15, 0); + \end{scope} + } + } + \end{tikzpicture} +\end{document} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: diff --git a/data/docs/source/images/triangular_lattice.pdf b/data/docs/source/images/triangular_lattice.pdf new file mode 100644 index 0000000000000000000000000000000000000000..a816cbed5097990b5777bf4b6acc6c14e6e9eb45 Binary files /dev/null and b/data/docs/source/images/triangular_lattice.pdf differ diff --git a/data/docs/source/images/triangular_lattice.svg b/data/docs/source/images/triangular_lattice.svg new file mode 100644 index 0000000000000000000000000000000000000000..1a0dbd7d9a62c6fb04fab9c64f04a64a583ef4aa --- /dev/null +++ b/data/docs/source/images/triangular_lattice.svg @@ -0,0 +1,828 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/data/docs/source/images/triangular_lattice.tex b/data/docs/source/images/triangular_lattice.tex new file mode 100644 index 0000000000000000000000000000000000000000..088bfe927deedaa6e2be2e556e70f054fd241cdb --- /dev/null +++ b/data/docs/source/images/triangular_lattice.tex @@ -0,0 +1,130 @@ +\documentclass[tikz]{standalone} + +\usepackage{amsfonts} +\usepackage{amsmath} +\usepackage{braket} + +\usepackage{tikz} +\usetikzlibrary{calc, decorations, positioning} + +\definecolor{googleR}{HTML}{DB4437} +\definecolor{googleG}{HTML}{0F9D58} +\definecolor{googleB}{HTML}{4285F4} + +% Main Document +\begin{document} +\begin{tikzpicture} + \def\clipX{2.00} + \def\clipY{1.75} + \def\legLength{0.175} + \def\tensorSize{0.15} + \def\tensorShiftY{0.0} + + % ------------------------ + % triangular lattice sites + % ------------------------ + + % define coordinates for the triangular lattice + \coordinate (T1) at ({-1.0*cos(30)}, {+2.0*cos(30)*tan(60)/2}); + \coordinate (T2) at ({+1.0*cos(30)}, {+2.0*cos(30)*tan(60)/2}); + \coordinate (T3) at ({-2.0*cos(30)}, {+0.0*cos(30)*tan(60)/2}); + \coordinate (T4) at ({-0.0*cos(30)}, {+0.0*cos(30)*tan(60)/2}); + \coordinate (T5) at ({+2.0*cos(30)}, {+0.0*cos(30)*tan(60)/2}); + \coordinate (T6) at ({-1.0*cos(30)}, {-2.0*cos(30)*tan(60)/2}); + \coordinate (T7) at ({+1.0*cos(30)}, {-2.0*cos(30)*tan(60)/2}); + + \coordinate (C1) at ($(T1) + ({-0.5*cos(30)}, {+1.0*cos(30)*tan(60)/2})$); + \coordinate (T1b) at ($(T1) + ({+0.5*cos(30)}, {+1.0*cos(30)*tan(60)/2})$); + \coordinate (T1a) at ($(T2) + ({-0.5*cos(30)}, {+1.0*cos(30)*tan(60)/2})$); + \coordinate (C2) at ($(T2) + ({+0.5*cos(30)}, {+1.0*cos(30)*tan(60)/2})$); + \coordinate (T2b) at ($(T2) + ({+1.0*cos(30)}, 0)$); + \coordinate (T2a) at ($(T5) + ({+0.5*cos(30)}, {+1.0*cos(30)*tan(60)/2})$); + \coordinate (C3) at ($(T5) + ({+1.0*cos(30)}, 0)$); + \coordinate (T3b) at ($(T5) + ({+0.5*cos(30)}, {-1.0*cos(30)*tan(60)/2})$); + \coordinate (T3a) at ($(T7) + ({+1.0*cos(30)}, 0)$); + \coordinate (C4) at ($(T7) + ({+0.5*cos(30)}, {-1.0*cos(30)*tan(60)/2})$); + \coordinate (T4b) at ($(T7) + ({-0.5*cos(30)}, {-1.0*cos(30)*tan(60)/2})$); + \coordinate (T4a) at ($(T6) + ({+0.5*cos(30)}, {-1.0*cos(30)*tan(60)/2})$); + \coordinate (C5) at ($(T6) + ({-0.5*cos(30)}, {-1.0*cos(30)*tan(60)/2})$); + \coordinate (T5b) at ($(T6) + ({-1.0*cos(30)}, 0)$); + \coordinate (T5a) at ($(T3) + ({-0.5*cos(30)}, {-1.0*cos(30)*tan(60)/2})$); + \coordinate (C6) at ($(T3) + ({-1.0*cos(30)}, 0)$); + \coordinate (T6b) at ($(T3) + ({-0.5*cos(30)}, {+1.0*cos(30)*tan(60)/2})$); + \coordinate (T6a) at ($(T1) + ({-1.0*cos(30)}, 0)$); + + \node at ($(T1) + ({-1.50*cos(30)}, {-0.0*cos(30)*tan(60)/2})$) {$\hdots$}; + \node[rotate = -60] at ($(T1) + ({-0.75*cos(30)}, {+1.5*cos(30)*tan(60)/2})$) {$\hdots$}; + \node[rotate = +60] at ($(T1) + ({+0.75*cos(30)}, {+1.5*cos(30)*tan(60)/2})$) {$\hdots$}; + + \node at ($(T2) + ({+1.50*cos(30)}, {-0.0*cos(30)*tan(60)/2})$) {$\hdots$}; + \node[rotate = -60] at ($(T2) + ({-0.75*cos(30)}, {+1.5*cos(30)*tan(60)/2})$) {$\hdots$}; + \node[rotate = +60] at ($(T2) + ({+0.75*cos(30)}, {+1.5*cos(30)*tan(60)/2})$) {$\hdots$}; + \node[rotate = -60] at ($(T2) + ({+0.75*cos(30)}, {-1.5*cos(30)*tan(60)/2})$) {$\hdots$}; + + \node[rotate = -60] at ($(T3) + ({-0.75*cos(30)}, {+1.5*cos(30)*tan(60)/2})$) {$\hdots$}; + \node at ($(T3) + ({-1.50*cos(30)}, {-0.0*cos(30)*tan(60)/2})$) {$\hdots$}; + \node[rotate = -60] at ($(T3) + ({+0.75*cos(30)}, {-1.5*cos(30)*tan(60)/2})$) {$\hdots$}; + \node[rotate = +60] at ($(T3) + ({-0.75*cos(30)}, {-1.5*cos(30)*tan(60)/2})$) {$\hdots$}; + + \node at ($(T4) + ({+1.50*cos(30)}, {-0.0*cos(30)*tan(60)/2})$) {$\hdots$}; + \node[rotate = -60] at ($(T4) + ({+0.75*cos(30)}, {-1.5*cos(30)*tan(60)/2})$) {$\hdots$}; + \node[rotate = +60] at ($(T4) + ({-0.75*cos(30)}, {-1.5*cos(30)*tan(60)/2})$) {$\hdots$}; + + \begin{scope}[shift = {(T1)}] + \begin{scope}[shift = {(0, +\tensorShiftY)}] + \draw[thick] (0,0) to ({-0.5*cos(30)}, {-1.0*cos(30)*tan(60)/2}); + \draw[thick] ({+0.5*cos(30)}, {+1.0*cos(30)*tan(60)/2}) to (0, 0); + \draw[thick] ({-0.5*cos(30)}, {+1.0*cos(30)*tan(60)/2}) to (0, 0); + \draw[thick] (0, 0) to ({+0.5*cos(30)}, {-1.0*cos(30)*tan(60)/2}); + \draw[thick] (0, 0) to ({-1.0*cos(30)}, 0); + \draw[thick] ({+1.0*cos(30)}, 0) to (0, 0); + \draw[thick] (0, 0) to (0, -\tensorShiftY - 0.5); + \draw[black, fill = googleB] (0, 0) circle (\tensorSize); + \end{scope} + \end{scope} + + \begin{scope}[shift = {(T2)}] + \begin{scope}[shift = {(0, +\tensorShiftY)}] + \draw[thick] (0,0) to ({-0.5*cos(30)}, {-1.0*cos(30)*tan(60)/2}); + \draw[thick] ({+0.5*cos(30)}, {+1.0*cos(30)*tan(60)/2}) to (0, 0); + \draw[thick] ({-0.5*cos(30)}, {+1.0*cos(30)*tan(60)/2}) to (0, 0); + \draw[thick] (0, 0) to ({+0.5*cos(30)}, {-1.0*cos(30)*tan(60)/2}); + \draw[thick] (0, 0) to ({-1.0*cos(30)}, 0); + \draw[thick] ({+1.0*cos(30)}, 0) to (0, 0); + \draw[thick] (0, 0) to (0, -\tensorShiftY - 0.5); + \draw[black, fill = googleB] (0, 0) circle (\tensorSize); + \end{scope} + \end{scope} + + \begin{scope}[shift = {(T3)}] + \begin{scope}[shift = {(0, +\tensorShiftY)}] + \draw[thick] (0,0) to ({-0.5*cos(30)}, {-1.0*cos(30)*tan(60)/2}); + \draw[thick] ({+0.5*cos(30)}, {+1.0*cos(30)*tan(60)/2}) to (0, 0); + \draw[thick] ({-0.5*cos(30)}, {+1.0*cos(30)*tan(60)/2}) to (0, 0); + \draw[thick] (0, 0) to ({+0.5*cos(30)}, {-1.0*cos(30)*tan(60)/2}); + \draw[thick] (0, 0) to ({-1.0*cos(30)}, 0); + \draw[thick] ({+1.0*cos(30)}, 0) to (0, 0); + \draw[thick] (0, 0) to (0, -\tensorShiftY - 0.5); + \draw[black, fill = googleB] (0, 0) circle (\tensorSize); + \end{scope} + \end{scope} + + \begin{scope}[shift = {(T4)}] + \begin{scope}[shift = {(0, +\tensorShiftY)}] + \draw[thick] (0,0) to ({-0.5*cos(30)}, {-1.0*cos(30)*tan(60)/2}); + \draw[thick] ({+0.5*cos(30)}, {+1.0*cos(30)*tan(60)/2}) to (0, 0); + \draw[thick] ({-0.5*cos(30)}, {+1.0*cos(30)*tan(60)/2}) to (0, 0); + \draw[thick] (0, 0) to ({+0.5*cos(30)}, {-1.0*cos(30)*tan(60)/2}); + \draw[thick] (0, 0) to ({-1.0*cos(30)}, 0); + \draw[thick] ({+1.0*cos(30)}, 0) to (0, 0); + \draw[thick] (0, 0) to (0, -\tensorShiftY - 0.5); + \draw[black, fill = googleB] (0, 0) circle (\tensorSize); + \end{scope} + \end{scope} +\end{tikzpicture} +\end{document} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: diff --git a/data/docs/source/images/triangular_structure.pdf b/data/docs/source/images/triangular_structure.pdf new file mode 100644 index 0000000000000000000000000000000000000000..d3ea7176f37db3290ee505a647336903f88dc54a Binary files /dev/null and b/data/docs/source/images/triangular_structure.pdf differ diff --git a/data/docs/source/images/triangular_structure.svg b/data/docs/source/images/triangular_structure.svg new file mode 100644 index 0000000000000000000000000000000000000000..c2c1eff86dac9dd2d6cbca979a7af64524ceb7a8 --- /dev/null +++ b/data/docs/source/images/triangular_structure.svg @@ -0,0 +1,1385 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/data/docs/source/images/triangular_structure.tex b/data/docs/source/images/triangular_structure.tex new file mode 100644 index 0000000000000000000000000000000000000000..832e2ceb54ad870daeae4e5f4681b9d110d6f8f6 --- /dev/null +++ b/data/docs/source/images/triangular_structure.tex @@ -0,0 +1,87 @@ +\documentclass[tikz]{standalone} + +\usepackage{amsfonts} +\usepackage{amsmath} +\usepackage{braket} + +\usepackage{tikz} +\usetikzlibrary{shapes.geometric,patterns,positioning,matrix} +\usetikzlibrary{shadows,calc,3d,arrows.meta,decorations.pathmorphing,decorations.markings,decorations.pathreplacing} + +\definecolor{googleB}{HTML}{4285F4} +\definecolor{googleG}{HTML}{34A853} +\definecolor{googleY}{HTML}{FBBC05} +\definecolor{googleR}{HTML}{EA4335} +\definecolor{googleBG}{HTML}{3B96A4} + +% load TikZ grafic definitions +%\input{gfx_TikZ} + +% main document +\begin{document} + + \begin{tikzpicture} + + \def\clipX{2.00} + \def\clipY{1.75} + \def\legLength{0.2} + \def\tensorSize{0.125} + \def\tensorSizeS{0.15} + + \begin{scope}[shift = {({3*cos(30)}, +5.25)}] + \draw[thick, -{Stealth[scale = 1.0]}] (0 : 0) to (270 : 1.0) node at (270 : 1.25) {$x$}; + \draw[thick, -{Stealth[scale = 1.0]}] (0 : 0) to ( 30 : 1.0) node at ( 30 : 1.25) {$y$}; + \end{scope} + + % \begin{scope}[shift = {(-4.25,{0.5*cos(30)*tan(60)/2}) to (+2,{1*cos(30)*tan(60)/2})}] + \begin{scope}[] + + \foreach \x/\y in {+3/-2, +6/0, +3/+2, +9/+2, +6/+4, +9/+6} { + \begin{scope}[shift = {({\x*cos(30)}, {\y*cos(30)*tan(60)/2}, 0)}] + + % virtual links triangular lattice + \coordinate (A) at (0, 0 , 0); + \coordinate (B) at ({2.0*cos(30)*cos(0)}, {2.0*cos(30)*sin(0)}, 0); + \coordinate (C) at ({2.0*cos(30)*cos(60)}, {2.0*cos(30)*sin(60)}, 0); + + \draw[gray, shift = {(A)}] ({-0.5*cos(30)},{-1.0*cos(30)*tan(60)/2},0) to ({+0.5*cos(30)},{+1.0*cos(30)*tan(60)/2},0); + \draw[gray, shift = {(A)}] ({-0.5*cos(30)},{+1.0*cos(30)*tan(60)/2},0) to ({+0.5*cos(30)},{-1.0*cos(30)*tan(60)/2},0); + \draw[gray, shift = {(A)}] ({-1.0*cos(30)}, 0, 0) to ({+1.0*cos(30)}, 0, 0); + + \draw[gray, shift = {(B)}] ({-0.5*cos(30)},{-1.0*cos(30)*tan(60)/2},0) to ({+0.5*cos(30)},{+1.0*cos(30)*tan(60)/2},0); + \draw[gray, shift = {(B)}] ({-0.5*cos(30)},{+1.0*cos(30)*tan(60)/2},0) to ({+0.5*cos(30)},{-1.0*cos(30)*tan(60)/2},0); + \draw[gray, shift = {(B)}] ({-1.0*cos(30)}, 0, 0) to ({+1.0*cos(30)}, 0, 0); + + \draw[gray, shift = {(C)}] ({-0.5*cos(30)},{-1.0*cos(30)*tan(60)/2},0) to ({+0.5*cos(30)},{+1.0*cos(30)*tan(60)/2},0); + \draw[gray, shift = {(C)}] ({-0.5*cos(30)},{+1.0*cos(30)*tan(60)/2},0) to ({+0.5*cos(30)},{-1.0*cos(30)*tan(60)/2},0); + \draw[gray, shift = {(C)}] ({-1.0*cos(30)}, 0, 0) to ({+1.0*cos(30)}, 0, 0); + + % lattice site + \draw[black, fill = white] (A) circle (\tensorSize); + \draw[black, fill = white] (B) circle (\tensorSize); + \draw[black, fill = white] (C) circle (\tensorSize); + + % draw coarse-grained tensor + \coordinate (D) at ({1.0*cos(30)}, {1.0*sin(30)}, 0); + \draw[thick] (D) to ($(D) + ({+1.5*cos(30)}, {+1.0*cos(30)*tan(60)/2}, 0)$); + \draw[thick] (D) to ($(D) + ({-1.5*cos(30)}, {-1.0*cos(30)*tan(60)/2}, 0)$); + \draw[thick] (D) to ($(D) + ({0}, {+2.0*cos(30)*tan(60)/2}, 0)$); + \draw[thick] (D) to ($(D) + ({0}, {-2.0*cos(30)*tan(60)/2}, 0)$); + \draw[thick, fill = googleB] (D) circle (\tensorSizeS); + + % draw unit cell boarders + \draw[very thick, gray, dotted, rounded corners = 5] ($(A) + (180 : 0.25)$) to ($(A) + (240 : 0.25)$) to ($(A) + (300 : 0.25)$) to ($(B) + (300 : 0.25)$) to ($(B) + ( 0 : 0.25)$) to ($(B) + ( 60 : 0.25)$) to ($(C) + ( 0 : 0.25)$) to ($(C) + ( 60 : 0.25)$) to ($(C) + (120 : 0.25)$) -- cycle; + + \end{scope} + } + + \end{scope} + + \end{tikzpicture} + +\end{document} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: diff --git a/data/docs/source/images/varipeps/Makefile b/data/docs/source/images/varipeps/Makefile new file mode 100644 index 0000000000000000000000000000000000000000..046340b4ea6ed6c2de639ef052e563a76619da9c --- /dev/null +++ b/data/docs/source/images/varipeps/Makefile @@ -0,0 +1,12 @@ +#!/usr/bin/make -f + +PDFS := $(wildcard *.pdf) +SVGS := $(PDFS:%.pdf=%.svg) + +all: ${SVGS} + +%.svg: %.pdf + inkscape --pdf-poppler "$<" -o "$@" + +clean: texauxclean + rm -f ${SVGS} diff --git a/data/docs/source/images/varipeps/ctmrgExample_1.pdf b/data/docs/source/images/varipeps/ctmrgExample_1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..0d63be3f665ea7932a53c8849419525f9aacab37 Binary files /dev/null and b/data/docs/source/images/varipeps/ctmrgExample_1.pdf differ diff --git a/data/docs/source/images/varipeps/ctmrgExample_1.svg b/data/docs/source/images/varipeps/ctmrgExample_1.svg new file mode 100644 index 0000000000000000000000000000000000000000..dd2811f1c71664e00cc6e4292878759c2edb9a3c --- /dev/null +++ b/data/docs/source/images/varipeps/ctmrgExample_1.svg @@ -0,0 +1,431 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/data/docs/source/images/varipeps/ctmrgExample_2.pdf b/data/docs/source/images/varipeps/ctmrgExample_2.pdf new file mode 100644 index 0000000000000000000000000000000000000000..57ef0762a42da108498b087ae68cd586fbf7f2d0 Binary files /dev/null and b/data/docs/source/images/varipeps/ctmrgExample_2.pdf differ diff --git a/data/docs/source/images/varipeps/ctmrgExample_2.svg b/data/docs/source/images/varipeps/ctmrgExample_2.svg new file mode 100644 index 0000000000000000000000000000000000000000..619d45567b056e04b34e32e1391dd0fd34b9ee96 --- /dev/null +++ b/data/docs/source/images/varipeps/ctmrgExample_2.svg @@ -0,0 +1,443 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/data/docs/source/index.rst b/data/docs/source/index.rst new file mode 100644 index 0000000000000000000000000000000000000000..acfd12c61744003c9ebdf4272a7c776be1b6741b --- /dev/null +++ b/data/docs/source/index.rst @@ -0,0 +1,40 @@ +.. figure:: /images/logo.* + :width: 50% + :alt: Logo of the variPEPS library with a triangular-PEPS norm as picture and + "variPEPS -- Variational PEPS Library" as text right of it + +Index +===== + +.. toctree:: + :maxdepth: 2 + :caption: Getting started + + general + +.. toctree:: + :maxdepth: 2 + :caption: variPEPS + + varipeps/varipeps + varipeps/unitcell + +.. toctree:: + :maxdepth: 2 + :caption: Examples + + examples/index + examples/heisenberg_afm_square + examples/heisenberg_afm_triangular + +.. toctree:: + :maxdepth: 2 + :caption: API documentation + + Public API Reference + +.. toctree:: + :maxdepth: 1 + :caption: Appendix + + license diff --git a/data/docs/source/license.rst b/data/docs/source/license.rst new file mode 100644 index 0000000000000000000000000000000000000000..d334b1e93e2dbc0e4ccb2df3b38ab92e7690b783 --- /dev/null +++ b/data/docs/source/license.rst @@ -0,0 +1,39 @@ +.. _license: + +License +======= + +.. _license_cc_by_sa: + +CC-BY-SA 4.0 +------------ + +This documentation, except for the API documentation (see below) and if not +marked otherwise, is licensed under the `CC BY-SA 4.0 +`_ license: + +.. include:: ../LICENSE + :literal: + +.. _license_cc_by: + +CC-BY 4.0 +--------- + +Parts of this documentation, if explicitly marked, are licensed under the `CC BY +4.0 `_ license: + +.. include:: varipeps/LICENSE_CC_BY_4.0 + :literal: + +.. _license_gpl_3: + +GPL-3.0-or-later +---------------- + +As the API documentation is automatically generated from the code, it is +licensed under the `GPL-3.0-or-later +`_: + +.. include:: ../../LICENSE + :literal: diff --git a/data/docs/source/varipeps/LICENSE_CC_BY_4.0 b/data/docs/source/varipeps/LICENSE_CC_BY_4.0 new file mode 100644 index 0000000000000000000000000000000000000000..4ea99c213c5c0c005ae4e80df8e52169d06896ec --- /dev/null +++ b/data/docs/source/varipeps/LICENSE_CC_BY_4.0 @@ -0,0 +1,395 @@ +Attribution 4.0 International + +======================================================================= + +Creative Commons Corporation ("Creative Commons") is not a law firm and +does not provide legal services or legal advice. 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For +the avoidance of doubt, this paragraph does not form part of the +public licenses. + +Creative Commons may be contacted at creativecommons.org. diff --git a/data/docs/source/varipeps/unitcell.rst b/data/docs/source/varipeps/unitcell.rst new file mode 100644 index 0000000000000000000000000000000000000000..7afd09cefcae5333d607b7c9722e30eaaf4aea11 --- /dev/null +++ b/data/docs/source/varipeps/unitcell.rst @@ -0,0 +1,165 @@ +.. _varipeps_unitcell: + +iPEPS Unit Cells +================ + +Theoretical Overview +-------------------- + +The text in this section is mainly copied (and only slightly modifed) from the +publication `SciPost Phys. Lect. Notes 86 (2024) +`_ by Jan Naumann, Erik +Lennart Weerda, Matteo Rizzi, Jens Eisert and Philipp Schmoll. This section is +licensed under the :ref:`license_cc_by` as the original work. + +General iPEPS unit cell structure +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +We aim to simulate quantum many-body systems directly in the thermodynamic +limit. To this end, we consider a unit cell of lattice sites that is repeated +periodically over the infinite two-dimensional lattice. Reflecting this, the +general configurtions of the iPEPS Ansatz are defined with an arbitrary unit +cell of size :math:`(L_x, L_y)` on the square lattice. The lattice setup, +denoted by :math:`\mathcal{L}`, can be specified by a single matrix, which +uniquely determines the different lattice sites as well as their +arrangement. Let us consider a concrete example of an :math:`(L_x, L_y) = (2, +2)` state with only two and all four individual tensors, denoted by + +.. math:: + + \mathcal L_1 = \begin{pmatrix} A & B \\ B & A \end{pmatrix}, \hspace{0.5cm} + \mathcal L_2 = \begin{pmatrix} A & C \\ B & D \end{pmatrix}. + +.. subfigure:: AB + :align: center + :width: 75% + :layout-sm: A|B + + .. image:: ../images/varipeps/ctmrgExample_1.* + + .. image:: ../images/varipeps/ctmrgExample_2.* + + iPEPS ansätze with a unit cell of size :math:`(L_x, L_y) = (2, 2)` and only + two (left) and four (right) different tensors. + +The corresponding iPEPS ansätze are visualized in figure above. Here, the +rows/columns of :math:`\mathcal{L}` correspond to the :math:`x`/:math:`y` +lattice directions. The unit cell :math:`\mathcal{L}` is repeated periodically +to generate the full two-dimensional system. The bulk bond dimension of the +iPEPS tensors, denoted by :math:`\chi_B`, controls the accuracy of the +ansatz. An iPEPS state with :math:`N` different tensors in the unit cell +consists of :math:`N p \chi_B^4` variational parameters, which we aim to +optimize such that the iPEPS wave function represents an approximation of the +ground state of a specific Hamiltonian. The parameter :math:`p` denotes the +dimension of the physical Hilbert space, e.g., :math:`p = 2` for a system of +spin-:math:`1/2` particles. + +The right choice of the unit cell is crucial in order to capture the structure +of the targeted state. A mismatch of the ansatz could not only lead to a bad +estimate of the ground state, but also to no convergence in the CTMRG routine at +all. Different lattice configurations have to be evaluated for specific +problems to find the correct pattern. + + +Spiral PEPS ansatz +^^^^^^^^^^^^^^^^^^ + +To circumvent the problem of a fixed and a priori chosen unit cell structure, +recently an alternative description to the periodic structure has been proposed +(`Phys. Rev. Lett. 133, 176502 (2024) +`_). This approach is applicable +if the Hamiltonian has a certain global symmetry, where the additional degree of +freedom can be employed to reduce the description of the state to a subspace, +e.g. :math:`SU(2)` for spin-:math:`1/2` systems. Here the state is described by +the smallest possible unit cell, i.e. a single site for a square lattice, as +well as a product of local unitary operators parameterized by a wave vector +:math:`\mathbf{k} = (k_x, k_y)`. A fixed choice of the wave vector then +corresponds to the specification of a unit cell structure in the common iPEPS +setup. This approach allows for a variational optimization of the wave vector +along with the translationally invariant iPEPS tensor, removing the need to +choose a fixed unit cell structure altogether. + +Technical implementation +------------------------ + +.. role:: python(code) + :language: python + +This section is provided under the default :ref:`license_cc_by_sa` license of +the documentation. + +Initialization of unit cell +^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +The most usual way to initialize a unit cell + +.. code-block:: python + + # Unit cell structure + structure = [[0, 1, ...], ...] + + # Physical dimension + d: int = ... + + # iPEPS bond dimension + D: int = ... + + # Start value for enviroment bond dimension + startChi: int = ... + + # Data type for the tensors: `float` (real) or `complex` tensors + unitcell_dtype = ... + + # Maximal enviroment bond dimension + max_chi: int = ... + + # Type of iPEPS ansatz (SQUARE/SQUARE_SPLIT/TRIANGULAR) + peps_type: varipeps.peps.PEPS_Type = varipeps.peps.PEPS_Type.SQUARE, # Use square iPEPS ansatz + + # Create random initialization for the iPEPS unit cell + unitcell = varipeps.peps.PEPS_Unit_Cell.random( + structure=structure, # Unit cell structure + d=d, # Physical dimension + D=chiB, # iPEPS bond dimension + chi=startChi, # Start value for enviroment bond dimension + dtype=unitcell_dtype, # Data type for the tensors: `float` (real) or `complex` tensors + max_chi=max_chi, # Maximal enviroment bond dimension + peps_type=peps_type, # Type of iPEPS ansatz + ) + +Here we define the unit cell structure which is used to simulate our model. +Using the unit cell structure and the model parameter (see below), we can +generate an initial unit cell. Here we initialize the iPEPS tensors with random +numbers and we are using the above discussed square iPEPS ansatz. The structure +is supplied as matrix with different numbers encoding the different tensors +(:math:`A`/:math:`B`/:math:`C`/:math:`\dots` in the example above). + +Unit cell parameters +^^^^^^^^^^^^^^^^^^^^ + +In the above code block we already showcase the (most important) parameters for +a iPEPS unit cell. To describe them in more detail: + +* :python:`d`: The physical dimension of our iPEPS ansatz. E.g. :python:`d = 2` + for a spin-:math:`1/2` state. +* :python:`D`: The (bulk) bond dimension of the virtual links of our local iPEPS + tensors. Sometimes also called :math:`\chi_B`. +* :python:`chi`: The initial value of the environment bond dimension of the + CTMRG tensors. Sometimes also called :math:`\chi_E`. +* :python:`dtype`: The numerical data type used to represent the tensors. In the + default configuration of the library this can be :obj:`float` (or + equivalent :obj:`numpy.float64`) for real double-precision floating point + numbers or :obj:`complex` (or equivalent :obj:`numpy.complex128`) for + complex double-precision floating point numbers. +* :python:`max_chi`: The :obj:`varipeps` library supports a dynamical + increase/decrease of the environment bond dimension mainly based on some + heuristics around the truncation error of the truncated singular value + decomposition. This parameter selects a maximum value for the environment bond + dimension to ensure that the simulation stays within some computational and + memory limits. +* :python:`peps_type`: As hinted already, the :obj:`varipeps` library supports + different structures for the iPEPS ansatz and the environment structure. In + the above theoretical overview, we limited us to the most common square case + but we will discuss in other sections the split- and triangular CTMRG + variants. These different cases can be selected at initialization time using + this parameter. diff --git a/data/docs/source/varipeps/varipeps.rst b/data/docs/source/varipeps/varipeps.rst new file mode 100644 index 0000000000000000000000000000000000000000..76e706db3580ea2396a3c632362d868fdd779cf6 --- /dev/null +++ b/data/docs/source/varipeps/varipeps.rst @@ -0,0 +1,44 @@ +.. _varipeps: + +Variational iPEPS +================= + +The text in this section is mainly copied (and only slightly modifed) from the +publication `SciPost Phys. Lect. Notes 86 (2024) +`_ by Jan Naumann, Erik +Lennart Weerda, Matteo Rizzi, Jens Eisert and Philipp Schmoll. This section is +licensed under the :ref:`license_cc_by` as the original work. + +We seek to find the TN representation of the state vector +:math:`\ket{\psi}_\mathrm{TN}` that best approximates the true ground state +vector :math:`\ket{\psi_0}` of an Hamilton operator of the form + +.. math:: + + H = \sum_{j \in \Lambda} T_j (h) \, , + +where :math:`T_j` is the translation operator on the lattice :math:`\Lambda`, +and :math:`h` is a generic :math:`k`-local Hamiltonian, i.e., it includes an +arbitrary number of operators acting on lattice sites at most at a (lattice) +distance :math:`k` from a reference lattice point. Such a situation is very +common in condensed matter physics, to say the least. To this aim, we employ the +variational principle + +.. math:: + + \frac{\langle \psi \vert H \vert \psi \rangle}{\langle \psi \vert \psi + \rangle} \ge E_0 \hspace{0.5cm} \forall \, \ket{\psi}, + +and use an energy gradient with respect to the tensor coefficients to search for +the minimum -- the precise optimization strategy being discussed later. Such an +energy gradient is accessed by means of tools from *automatic differentiation* +(AD), a set of techniques to evaluate the derivative of a function specified by +a computer program. In the :obj:`varipeps` library we use the +:obj:`jax`-framework which already implements AS for common mathematical +functions. + +Since we directly target systems in the thermodynamic limit, a *corner transfer +matrix renormalization group* (CTMRG) procedure constitutes the backbone of the +algorithm, and also will come in handy for AD purposes. This is used to compute +the approximate contraction of the infinite lattice, which is crucial in order +to compute accurate expectation values in the first place. diff --git a/data/examples/README.md b/data/examples/README.md new file mode 100644 index 0000000000000000000000000000000000000000..2430ecf11cffe5698ed1b4a1ae0e700e255f0ff1 --- /dev/null +++ b/data/examples/README.md @@ -0,0 +1,9 @@ +# Examples + +In this folder we provide some examples how to use the variPEPS library. The +examples are provided as + +1. The raw Python script which can be just been executed by calling `python3 +