| import numpy as np |
| from scipy.sparse.linalg import LinearOperator, eigs |
|
|
| import jax.numpy as jnp |
|
|
| from varipeps.contractions import apply_contraction_jitted |
| from varipeps.peps import PEPS_Unit_Cell |
|
|
|
|
| def calculate_correlation_length(unitcell: PEPS_Unit_Cell, num_eigvals: int = 8): |
| if num_eigvals < 2: |
| raise ValueError( |
| "Number of eigenvalues must be at least two to compute the correlation length." |
| ) |
|
|
| initial_vector_left = apply_contraction_jitted( |
| "corrlength_vector_left", |
| (unitcell[0, 0][0][0].tensor,), |
| (unitcell[0, 0][0][0],), |
| (), |
| ) |
| initial_vector_left = initial_vector_left.reshape(-1) |
|
|
| initial_vector_top = apply_contraction_jitted( |
| "corrlength_vector_top", |
| (unitcell[0, 0][0][0].tensor,), |
| (unitcell[0, 0][0][0],), |
| (), |
| ) |
| initial_vector_top = initial_vector_top.reshape(-1) |
|
|
| def left_matvec(vec): |
| vec = jnp.asarray(vec) |
| for _, view in unitcell.iter_one_row(0): |
| if vec.ndim != 4: |
| vec = vec.reshape( |
| view[0, 0][0][0].T1.shape[0], |
| view[0, 0][0][0].tensor.shape[0], |
| view[0, 0][0][0].tensor.shape[0], |
| view[0, 0][0][0].T3.shape[0], |
| ) |
| vec = apply_contraction_jitted( |
| "corrlength_absorb_one_column", |
| (view[0, 0][0][0].tensor,), |
| (view[0, 0][0][0],), |
| (vec,), |
| ) |
| return vec.reshape(-1) |
|
|
| left_lin_op = LinearOperator( |
| (initial_vector_left.shape[0], initial_vector_left.shape[0]), |
| matvec=left_matvec, |
| ) |
|
|
| eig_left, eigvec_left = eigs( |
| left_lin_op, k=num_eigvals, v0=initial_vector_left, which="LM" |
| ) |
|
|
| eig_left = eig_left[np.argsort(np.abs(eig_left))[::-1]] |
| eig_left /= np.abs(eig_left[0]) |
|
|
| corr_len_left = -1 / np.log(np.abs(eig_left[1])) |
|
|
| def top_matvec(vec): |
| vec = jnp.asarray(vec) |
| for _, view in unitcell.iter_one_column(0): |
| if vec.ndim != 4: |
| vec = vec.reshape( |
| view[0, 0][0][0].T4.shape[3], |
| view[0, 0][0][0].tensor.shape[4], |
| view[0, 0][0][0].tensor.shape[4], |
| view[0, 0][0][0].T2.shape[3], |
| ) |
| vec = apply_contraction_jitted( |
| "corrlength_absorb_one_row", |
| (view[0, 0][0][0].tensor,), |
| (view[0, 0][0][0],), |
| (vec,), |
| ) |
| return vec.reshape(-1) |
|
|
| top_lin_op = LinearOperator( |
| (initial_vector_top.shape[0], initial_vector_top.shape[0]), |
| matvec=top_matvec, |
| ) |
|
|
| eig_top, eigvec_top = eigs( |
| top_lin_op, k=num_eigvals, v0=initial_vector_top, which="LM" |
| ) |
|
|
| eig_top = eig_top[np.argsort(np.abs(eig_top))[::-1]] |
| eig_top /= np.abs(eig_top[0]) |
|
|
| corr_len_top = -1 / np.log(np.abs(eig_top[1])) |
|
|
| return (corr_len_left, eig_left), (corr_len_top, eig_top) |
|
|
