data/varipeps/expectation/helpers.py

import jax.numpy as jnp
from jax import jit

from varipeps.peps import PEPS_Tensor
from varipeps.contractions import apply_contraction, Definitions

from typing import Sequence, Tuple


def partially_traced_four_site_density_matrices(
    peps_tensors: Sequence[jnp.ndarray],
    peps_tensor_objs: Sequence[PEPS_Tensor],
    real_physical_dimension: int,
    num_coarse_grained_physical_indices: int,
    open_physical_indices: Tuple[Tuple[int], Tuple[int], Tuple[int], Tuple[int]],
) -> Tuple[jnp.ndarray, jnp.ndarray, jnp.ndarray, jnp.ndarray]:

    if not all(
        all(isinstance(open_idx, int) for open_idx in tup) or len(tup) == 0
        for tup in open_physical_indices
    ):
        raise TypeError(
            "All elements of each tuple must be integers (or the tuple may be empty)."
        )
    if not all(
        len(tup) <= num_coarse_grained_physical_indices for tup in open_physical_indices
    ):
        raise ValueError(
            f"At least one tuple in `open_physical_indices` {open_physical_indices} has length greater"
            f"than the number of coarse-grained physical sites {num_coarse_grained_physical_indices}"
        )
    peps_tensors = [
        t.reshape(
            t.shape[0],
            t.shape[1],
            *((real_physical_dimension,) * num_coarse_grained_physical_indices),
            t.shape[3],
            t.shape[4],
        )
        for t in peps_tensors
    ]
    t_top_left, t_top_right, t_bottom_left, t_bottom_right = peps_tensors
    t_obj_top_left, t_obj_top_right, t_obj_bottom_left, t_obj_bottom_right = (
        peps_tensor_objs
    )
    top_left_i, top_right_i, bottom_left_i, bottom_right_i = open_physical_indices

    if any(
        not hasattr(
            Definitions,
            (
                f"partially_traced_four_site_density_matrices_{pos_name}_"
                f"{real_physical_dimension}_{num_coarse_grained_physical_indices}_{pos_idx}"
            ),
        )
        for pos_idx, pos_name in zip(
            open_physical_indices,
            ["top_left", "top_right", "bottom_left", "bottom_right"],
            strict=True,
        )
    ):

        phys_contraction_i_top_left = list(
            range(7, 7 + num_coarse_grained_physical_indices - len(top_left_i))
        )
        phys_contraction_i_conj_top_left = list(
            range(7, 7 + num_coarse_grained_physical_indices - len(top_left_i))
        )
        for pos, i in enumerate(top_left_i):
            phys_contraction_i_top_left.insert(i - 1, -(pos + 1))
            phys_contraction_i_conj_top_left.insert(i - 1, -len(top_left_i) - (pos + 1))
        phys_contraction_i_top_left = tuple(phys_contraction_i_top_left)
        phys_contraction_i_conj_top_left = tuple(phys_contraction_i_conj_top_left)

        contraction_top_left = {
            "tensors": [["tensor", "tensor_conj", "T4", "C1", "T1"]],
            "network": [
                [
                    (3, -2 * len(top_left_i) - 2)
                    + phys_contraction_i_top_left
                    + (-2 * len(top_left_i) - 5, 4),  # tensor
                    (5, -2 * len(top_left_i) - 3)
                    + phys_contraction_i_conj_top_left
                    + (-2 * len(top_left_i) - 6, 6),  # tensor_conj
                    (-2 * len(top_left_i) - 1, 5, 3, 1),  # T4
                    (1, 2),  # C1
                    (2, 4, 6, -2 * len(top_left_i) - 4),  # T1
                ]
            ],
        }
        Definitions.add_def(
            (
                f"partially_traced_four_site_density_matrices_top_left_"
                f"{real_physical_dimension}_{num_coarse_grained_physical_indices}_{top_left_i}"
            ),
            contraction_top_left,
        )

        phys_contraction_i_top_right = list(
            range(7, 7 + num_coarse_grained_physical_indices - len(top_right_i))
        )
        phys_contraction_i_conj_top_right = list(
            range(7, 7 + num_coarse_grained_physical_indices - len(top_right_i))
        )
        for pos, i in enumerate(top_right_i):
            phys_contraction_i_top_right.insert(i - 1, -(pos + 1))
            phys_contraction_i_conj_top_right.insert(
                i - 1, -len(top_right_i) - (pos + 1)
            )
        phys_contraction_i_top_right = tuple(phys_contraction_i_top_right)
        phys_contraction_i_conj_top_right = tuple(phys_contraction_i_conj_top_right)

        contraction_top_right = {
            "tensors": [["tensor", "tensor_conj", "T1", "C2", "T2"]],
            "network": [
                # With rotational consistent output order (ChiE, Ket chiB, Bra chiB)
                [
                    (-2 * len(top_right_i) - 2, -2 * len(top_right_i) - 5)
                    + phys_contraction_i_top_right
                    + (4, 3),  # tensor
                    (-2 * len(top_right_i) - 3, -2 * len(top_right_i) - 6)
                    + phys_contraction_i_conj_top_right
                    + (6, 5),  # tensor_conj
                    (-2 * len(top_right_i) - 1, 3, 5, 1),  # T1
                    (1, 2),  # C2
                    (4, 6, -2 * len(top_right_i) - 4, 2),  # T2
                ]
                # Without rotational consistent output order
                # [
                #     (-2 * len(top_right_i) - 2, -2 * len(top_right_i) - 6)
                #     + phys_contraction_i_top_right
                #     + (4, 3),  # tensor
                #     (-2 * len(top_right_i) - 3, -2 * len(top_right_i) - 5)
                #     + phys_contraction_i_conj_top_right
                #     + (6, 5),  # tensor_conj
                #     (-2 * len(top_right_i) - 1, 3, 5, 1),  # T1
                #     (1, 2),  # C2
                #     (4, 6, -2 * len(top_right_i) - 4, 2),  # T2
                # ]
            ],
        }
        Definitions.add_def(
            (
                f"partially_traced_four_site_density_matrices_top_right_"
                f"{real_physical_dimension}_{num_coarse_grained_physical_indices}_{top_right_i}"
            ),
            contraction_top_right,
        )

        phys_contraction_i_bottom_left = list(
            range(7, 7 + num_coarse_grained_physical_indices - len(bottom_left_i))
        )
        phys_contraction_i_conj_bottom_left = list(
            range(7, 7 + num_coarse_grained_physical_indices - len(bottom_left_i))
        )
        for pos, i in enumerate(bottom_left_i):
            phys_contraction_i_bottom_left.insert(i - 1, -(pos + 1))
            phys_contraction_i_conj_bottom_left.insert(
                i - 1, -len(bottom_left_i) - (pos + 1)
            )
        phys_contraction_i_bottom_left = tuple(phys_contraction_i_bottom_left)
        phys_contraction_i_conj_bottom_left = tuple(phys_contraction_i_conj_bottom_left)

        contraction_bottom_left = {
            "tensors": [["tensor", "tensor_conj", "T3", "C4", "T4"]],
            "network": [
                # With rotational consistent output order (ChiE, Ket chiB, Bra chiB)
                [
                    (3, 4)
                    + phys_contraction_i_bottom_left
                    + (
                        -2 * len(bottom_left_i) - 2,
                        -2 * len(bottom_left_i) - 5,
                    ),  # tensor
                    (5, 6)
                    + phys_contraction_i_conj_bottom_left
                    + (
                        -2 * len(bottom_left_i) - 3,
                        -2 * len(bottom_left_i) - 6,
                    ),  # tensor_conj
                    (2, -2 * len(bottom_left_i) - 1, 6, 4),  # T3
                    (2, 1),  # C4
                    (1, 5, 3, -2 * len(bottom_left_i) - 4),  # T4
                ]
                # Without rotational consistent output order
                # [
                #     (3, 4)
                #     + phys_contraction_i_bottom_left
                #     + (
                #         -2 * len(bottom_left_i) - 3,
                #         -2 * len(bottom_left_i) - 5,
                #     ),  # tensor
                #     (5, 6)
                #     + phys_contraction_i_conj_bottom_left
                #     + (
                #         -2 * len(bottom_left_i) - 2,
                #         -2 * len(bottom_left_i) - 6,
                #     ),  # tensor_conj
                #     (2, -2 * len(bottom_left_i) - 1, 6, 4),  # T3
                #     (2, 1),  # C4
                #     (1, 5, 3, -2 * len(bottom_left_i) - 4),  # T4
                # ]
            ],
        }
        Definitions.add_def(
            (
                f"partially_traced_four_site_density_matrices_bottom_left_"
                f"{real_physical_dimension}_{num_coarse_grained_physical_indices}_{bottom_left_i}"
            ),
            contraction_bottom_left,
        )

        phys_contraction_i_bottom_right = list(
            range(7, 7 + num_coarse_grained_physical_indices - len(bottom_right_i))
        )
        phys_contraction_i_conj_bottom_right = list(
            range(7, 7 + num_coarse_grained_physical_indices - len(bottom_right_i))
        )
        for pos, i in enumerate(bottom_right_i):
            phys_contraction_i_bottom_right.insert(i - 1, -(pos + 1))
            phys_contraction_i_conj_bottom_right.insert(
                i - 1, -len(bottom_right_i) - (pos + 1)
            )
        phys_contraction_i_bottom_right = tuple(phys_contraction_i_bottom_right)
        phys_contraction_i_conj_bottom_right = tuple(
            phys_contraction_i_conj_bottom_right
        )

        contraction_bottom_right = {
            "tensors": [["tensor", "tensor_conj", "T2", "T3", "C3"]],
            "network": [
                # With rotational consistent output order (ChiE, Ket chiB, Bra chiB)
                [
                    (-2 * len(bottom_right_i) - 5, 3)
                    + phys_contraction_i_bottom_right
                    + (4, -2 * len(bottom_right_i) - 2),  # tensor
                    (-2 * len(bottom_right_i) - 6, 5)
                    + phys_contraction_i_conj_bottom_right
                    + (6, -2 * len(bottom_right_i) - 3),  # tensor_conj
                    (4, 6, 2, -2 * len(bottom_right_i) - 1),  # T2
                    (-2 * len(bottom_right_i) - 4, 1, 5, 3),  # T3
                    (1, 2),  # C3
                ]
                # Without rotational consistent output order
                # [
                #     (-2 * len(bottom_right_i) - 6, 3)
                #     + phys_contraction_i_bottom_right
                #     + (4, -2 * len(bottom_right_i) - 3),  # tensor
                #     (-2 * len(bottom_right_i) - 5, 5)
                #     + phys_contraction_i_conj_bottom_right
                #     + (6, -2 * len(bottom_right_i) - 2),  # tensor_conj
                #     (4, 6, 2, -2 * len(bottom_right_i) - 1),  # T2
                #     (-2 * len(bottom_right_i) - 4, 1, 5, 3),  # T3
                #     (1, 2),  # C3
                # ]
            ],
        }
        Definitions.add_def(
            (
                f"partially_traced_four_site_density_matrices_bottom_right_"
                f"{real_physical_dimension}_{num_coarse_grained_physical_indices}_{bottom_right_i}"
            ),
            contraction_bottom_right,
        )

    density_top_left = apply_contraction(
        (
            f"partially_traced_four_site_density_matrices_top_left_"
            f"{real_physical_dimension}_{num_coarse_grained_physical_indices}_{top_left_i}"
        ),
        [t_top_left],
        [t_obj_top_left],
        [],
        disable_identity_check=True,
    )
    if len(top_left_i) > 0:
        density_top_left = density_top_left.reshape(
            real_physical_dimension ** len(top_left_i),
            real_physical_dimension ** len(top_left_i),
            density_top_left.shape[-6],
            density_top_left.shape[-5],
            density_top_left.shape[-4],
            density_top_left.shape[-3],
            density_top_left.shape[-2],
            density_top_left.shape[-1],
        )

    density_top_right = apply_contraction(
        (
            f"partially_traced_four_site_density_matrices_top_right_"
            f"{real_physical_dimension}_{num_coarse_grained_physical_indices}_{top_right_i}"
        ),
        [t_top_right],
        [t_obj_top_right],
        [],
        disable_identity_check=True,
    )
    if len(top_right_i) > 0:
        density_top_right = density_top_right.reshape(
            real_physical_dimension ** len(top_right_i),
            real_physical_dimension ** len(top_right_i),
            density_top_right.shape[-6],
            density_top_right.shape[-5],
            density_top_right.shape[-4],
            density_top_right.shape[-3],
            density_top_right.shape[-2],
            density_top_right.shape[-1],
        )

    density_bottom_left = apply_contraction(
        (
            f"partially_traced_four_site_density_matrices_bottom_left_"
            f"{real_physical_dimension}_{num_coarse_grained_physical_indices}_{bottom_left_i}"
        ),
        [t_bottom_left],
        [t_obj_bottom_left],
        [],
        disable_identity_check=True,
    )
    if len(bottom_left_i) > 0:
        density_bottom_left = density_bottom_left.reshape(
            real_physical_dimension ** len(bottom_left_i),
            real_physical_dimension ** len(bottom_left_i),
            density_bottom_left.shape[-6],
            density_bottom_left.shape[-5],
            density_bottom_left.shape[-4],
            density_bottom_left.shape[-3],
            density_bottom_left.shape[-2],
            density_bottom_left.shape[-1],
        )

    density_bottom_right = apply_contraction(
        (
            f"partially_traced_four_site_density_matrices_bottom_right_"
            f"{real_physical_dimension}_{num_coarse_grained_physical_indices}_{bottom_right_i}"
        ),
        [t_bottom_right],
        [t_obj_bottom_right],
        [],
        disable_identity_check=True,
    )
    if len(bottom_right_i) > 0:
        density_bottom_right = density_bottom_right.reshape(
            real_physical_dimension ** len(bottom_right_i),
            real_physical_dimension ** len(bottom_right_i),
            density_bottom_right.shape[-6],
            density_bottom_right.shape[-5],
            density_bottom_right.shape[-4],
            density_bottom_right.shape[-3],
            density_bottom_right.shape[-2],
            density_bottom_right.shape[-1],
        )

    return (
        density_top_left,
        density_top_right,
        density_bottom_left,
        density_bottom_right,
    )


def partially_traced_horizontal_two_site_density_matrices(
    peps_tensors: Sequence[jnp.ndarray],
    peps_tensor_objs: Sequence[PEPS_Tensor],
    real_physical_dimension: int,
    num_coarse_grained_physical_indices: int,
    open_physical_indices: Tuple[Tuple[int], Tuple[int]],
) -> Tuple[jnp.ndarray, jnp.ndarray]:

    if not all(
        all(isinstance(open_idx, int) for open_idx in tup) or len(tup) == 0
        for tup in open_physical_indices
    ):
        raise TypeError(
            "All elements of each tuple must be integers (or the tuple may be empty)."
        )
    if not all(
        len(tup) <= num_coarse_grained_physical_indices for tup in open_physical_indices
    ):
        raise ValueError(
            f"At least one tuple in `open_physical_indices` {open_physical_indices} has length greater"
            f"than the number of coarse-grained physical sites {num_coarse_grained_physical_indices}"
        )
    peps_tensors = [
        t.reshape(
            t.shape[0],
            t.shape[1],
            *((real_physical_dimension,) * num_coarse_grained_physical_indices),
            t.shape[3],
            t.shape[4],
        )
        for t in peps_tensors
    ]
    t_left, t_right = peps_tensors
    t_obj_left, t_obj_right = peps_tensor_objs
    left_i, right_i = open_physical_indices

    if any(
        not hasattr(
            Definitions,
            (
                f"partially_traced_horizontal_two_site_density_matrices_{pos_name}_"
                f"{real_physical_dimension}_{num_coarse_grained_physical_indices}_{pos_idx}"
            ),
        )
        for pos_idx, pos_name in zip(
            open_physical_indices, ["left", "right"], strict=True
        )
    ):

        phys_contraction_i_left = list(
            range(11, 11 + num_coarse_grained_physical_indices - len(left_i))
        )
        phys_contraction_i_conj_left = list(
            range(11, 11 + num_coarse_grained_physical_indices - len(left_i))
        )
        for pos, i in enumerate(left_i):
            phys_contraction_i_left.insert(i - 1, -(pos + 1))
            phys_contraction_i_conj_left.insert(i - 1, -len(left_i) - (pos + 1))
        phys_contraction_i_left = tuple(phys_contraction_i_left)
        phys_contraction_i_conj_left = tuple(phys_contraction_i_conj_left)

        contraction_left = {
            "tensors": [["tensor", "tensor_conj", "C1", "T1", "T3", "C4", "T4"]],
            "network": [
                [
                    (5, 9)
                    + phys_contraction_i_left
                    + (-2 * len(left_i) - 2, 4),  # tensor
                    (7, 10)
                    + phys_contraction_i_conj_left
                    + (-2 * len(left_i) - 3, 6),  # tensor_conj
                    (1, 3),  # C1
                    (3, 4, 6, -2 * len(left_i) - 1),  # T1
                    (2, -2 * len(left_i) - 4, 10, 9),  # T3
                    (2, 8),  # C4
                    (8, 7, 5, 1),  # T4
                ]
            ],
        }
        Definitions.add_def(
            (
                f"partially_traced_horizontal_two_site_density_matrices_left_"
                f"{real_physical_dimension}_{num_coarse_grained_physical_indices}_{left_i}"
            ),
            contraction_left,
        )

        phys_contraction_i_right = list(
            range(11, 11 + num_coarse_grained_physical_indices - len(right_i))
        )
        phys_contraction_i_conj_right = list(
            range(11, 11 + num_coarse_grained_physical_indices - len(right_i))
        )
        for pos, i in enumerate(right_i):
            phys_contraction_i_right.insert(i - 1, -4 - (pos + 1))
            phys_contraction_i_conj_right.insert(i - 1, -4 - len(right_i) - (pos + 1))
        phys_contraction_i_right = tuple(phys_contraction_i_right)
        phys_contraction_i_conj_right = tuple(phys_contraction_i_conj_right)

        contraction_right = {
            "tensors": [["tensor", "tensor_conj", "T1", "C2", "T2", "T3", "C3"]],
            "network": [
                [
                    (-2, 8) + phys_contraction_i_right + (5, 4),  # tensor
                    (-3, 9) + phys_contraction_i_conj_right + (7, 6),  # tensor_conj
                    (-1, 4, 6, 3),  # T1
                    (3, 1),  # C2
                    (5, 7, 10, 1),  # T2
                    (-4, 2, 9, 8),  # T3
                    (2, 10),  # C3
                ]
            ],
        }
        Definitions.add_def(
            (
                f"partially_traced_horizontal_two_site_density_matrices_right_"
                f"{real_physical_dimension}_{num_coarse_grained_physical_indices}_{right_i}"
            ),
            contraction_right,
        )

    density_left = apply_contraction(
        (
            f"partially_traced_horizontal_two_site_density_matrices_left_"
            f"{real_physical_dimension}_{num_coarse_grained_physical_indices}_{left_i}"
        ),
        [t_left],
        [t_obj_left],
        [],
        disable_identity_check=True,
    )
    if len(left_i) > 0:
        density_left = density_left.reshape(
            real_physical_dimension ** len(left_i),
            real_physical_dimension ** len(left_i),
            density_left.shape[-4],
            density_left.shape[-3],
            density_left.shape[-2],
            density_left.shape[-1],
        )

    density_right = apply_contraction(
        (
            f"partially_traced_horizontal_two_site_density_matrices_right_"
            f"{real_physical_dimension}_{num_coarse_grained_physical_indices}_{right_i}"
        ),
        [t_right],
        [t_obj_right],
        [],
        disable_identity_check=True,
    )
    if len(right_i) > 0:
        # Physical indices are at the end (ket, bra), for consistency with _two_site_workhorse
        density_right = density_right.reshape(
            density_right.shape[0],
            density_right.shape[1],
            density_right.shape[2],
            density_right.shape[3],
            real_physical_dimension ** len(right_i),
            real_physical_dimension ** len(right_i),
        )

    return (
        density_left,
        density_right,
    )


def partially_traced_vertical_two_site_density_matrices(
    peps_tensors: Sequence[jnp.ndarray],
    peps_tensor_objs: Sequence[PEPS_Tensor],
    real_physical_dimension: int,
    num_coarse_grained_physical_indices: int,
    open_physical_indices: Tuple[Tuple[int], Tuple[int]],
) -> Tuple[jnp.ndarray, jnp.ndarray]:

    if not all(
        all(isinstance(open_idx, int) for open_idx in tup) or len(tup) == 0
        for tup in open_physical_indices
    ):
        raise TypeError(
            "All elements of each tuple must be integers (or the tuple may be empty)."
        )
    if not all(
        len(tup) <= num_coarse_grained_physical_indices for tup in open_physical_indices
    ):
        raise ValueError(
            f"At least one tuple in `open_physical_indices` {open_physical_indices} has length greater"
            f"than the number of coarse-grained physical sites {num_coarse_grained_physical_indices}"
        )
    peps_tensors = [
        t.reshape(
            t.shape[0],
            t.shape[1],
            *((real_physical_dimension,) * num_coarse_grained_physical_indices),
            t.shape[3],
            t.shape[4],
        )
        for t in peps_tensors
    ]
    t_top, t_bottom = peps_tensors
    t_obj_top, t_obj_bottom = peps_tensor_objs
    top_i, bottom_i = open_physical_indices

    if any(
        not hasattr(
            Definitions,
            (
                f"partially_traced_vertical_two_site_density_matrices_{pos_name}_"
                f"{real_physical_dimension}_{num_coarse_grained_physical_indices}_{pos_idx}"
            ),
        )
        for pos_idx, pos_name in zip(
            open_physical_indices, ["top", "bottom"], strict=True
        )
    ):

        phys_contraction_i_top = list(
            range(11, 11 + num_coarse_grained_physical_indices - len(top_i))
        )
        phys_contraction_i_conj_top = list(
            range(11, 11 + num_coarse_grained_physical_indices - len(top_i))
        )
        for pos, i in enumerate(top_i):
            phys_contraction_i_top.insert(i - 1, -(pos + 1))
            phys_contraction_i_conj_top.insert(i - 1, -len(top_i) - (pos + 1))
        phys_contraction_i_top = tuple(phys_contraction_i_top)
        phys_contraction_i_conj_top = tuple(phys_contraction_i_conj_top)

        contraction_top = {
            "tensors": [["tensor", "tensor_conj", "C1", "T1", "C2", "T2", "T4"]],
            "network": [
                [
                    (8, -2 * len(top_i) - 2)
                    + phys_contraction_i_top
                    + (4, 5),  # tensor
                    (9, -2 * len(top_i) - 3)
                    + phys_contraction_i_conj_top
                    + (6, 7),  # tensor_conj
                    (2, 10),  # C1
                    (10, 5, 7, 1),  # T1
                    (1, 3),  # C2
                    (4, 6, -2 * len(top_i) - 4, 3),  # T2
                    (-2 * len(top_i) - 1, 9, 8, 2),  # T4
                ]
            ],
        }
        Definitions.add_def(
            (
                f"partially_traced_vertical_two_site_density_matrices_top_"
                f"{real_physical_dimension}_{num_coarse_grained_physical_indices}_{top_i}"
            ),
            contraction_top,
        )

        phys_contraction_i_bottom = list(
            range(11, 11 + num_coarse_grained_physical_indices - len(bottom_i))
        )
        phys_contraction_i_conj_bottom = list(
            range(11, 11 + num_coarse_grained_physical_indices - len(bottom_i))
        )
        for pos, i in enumerate(bottom_i):
            phys_contraction_i_bottom.insert(i - 1, -4 - (pos + 1))
            phys_contraction_i_conj_bottom.insert(i - 1, -4 - len(bottom_i) - (pos + 1))
        phys_contraction_i_bottom = tuple(phys_contraction_i_bottom)
        phys_contraction_i_conj_bottom = tuple(phys_contraction_i_conj_bottom)

        contraction_bottom = {
            "tensors": [["tensor", "tensor_conj", "T2", "C3", "T3", "C4", "T4"]],
            "network": [
                [
                    (4, 5) + phys_contraction_i_bottom + (8, -2),  # tensor
                    (6, 7) + phys_contraction_i_conj_bottom + (9, -3),  # tensor_conj
                    (8, 9, 2, -4),  # T2
                    (10, 2),  # C3
                    (1, 10, 7, 5),  # T3
                    (1, 3),  # C4
                    (3, 6, 4, -1),  # T4
                ]
            ],
        }
        Definitions.add_def(
            (
                f"partially_traced_vertical_two_site_density_matrices_bottom_"
                f"{real_physical_dimension}_{num_coarse_grained_physical_indices}_{bottom_i}"
            ),
            contraction_bottom,
        )

    density_top = apply_contraction(
        (
            f"partially_traced_vertical_two_site_density_matrices_top_"
            f"{real_physical_dimension}_{num_coarse_grained_physical_indices}_{top_i}"
        ),
        [t_top],
        [t_obj_top],
        [],
        disable_identity_check=True,
    )
    if len(top_i) > 0:
        density_top = density_top.reshape(
            real_physical_dimension ** len(top_i),
            real_physical_dimension ** len(top_i),
            density_top.shape[-4],
            density_top.shape[-3],
            density_top.shape[-2],
            density_top.shape[-1],
        )

    density_bottom = apply_contraction(
        (
            f"partially_traced_vertical_two_site_density_matrices_bottom_"
            f"{real_physical_dimension}_{num_coarse_grained_physical_indices}_{bottom_i}"
        ),
        [t_bottom],
        [t_obj_bottom],
        [],
        disable_identity_check=True,
    )
    if len(bottom_i) > 0:
        # Physical indices are at the end (ket, bra), for consistency with _two_site_workhorse
        density_bottom = density_bottom.reshape(
            density_bottom.shape[0],
            density_bottom.shape[1],
            density_bottom.shape[2],
            density_bottom.shape[3],
            real_physical_dimension ** len(bottom_i),
            real_physical_dimension ** len(bottom_i),
        )

    return (
        density_top,
        density_bottom,
    )