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Implement next-nearest interaction for triangular lattice
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‎docs/source/api/expectation/four_sites.rst

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.. _varipeps_expectation_four_sites:
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.. currentmodule:: varipeps.expectation.four_sites
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Calculation of four sites expectation values
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============================================
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.. automodule:: varipeps.expectation.four_sites
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:members:
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:undoc-members:
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:show-inheritance:
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:special-members: __call__

‎docs/source/api/expectation/index.rst

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@@ -14,6 +14,7 @@ Calculation of expectation values (:mod:`varipeps.expectation`)
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one_site
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two_sites
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three_sites
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four_sites
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spiral_helpers
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.. automodule:: varipeps.expectation

‎varipeps/contractions/definitions.py

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@@ -503,6 +503,67 @@ def _prepare_defs(cls):
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],
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}
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density_matrix_two_sites_horizontal_rectangle: Definition = {
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"tensors": [
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["tensor", "tensor_conj", "T1"], # top_middle
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["tensor", "tensor_conj", "T3"], # bottom_middle
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"top_left",
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"top_right",
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"bottom_left",
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"bottom_right",
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],
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"network": [
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[
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(5, 11, 9, 19, 6), # tensor
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(7, 13, 9, 20, 8), # tensor_conj
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(4, 6, 8, 18), # T1
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],
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[
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(10, 16, 14, 25, 11), # tensor
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(12, 17, 14, 26, 13), # tensor_conj
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(15, 24, 17, 16), # T3
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],
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(-1, -3, 1, 2, 3, 4, 5, 7), # top_left
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(18, 19, 20, 21, 22, 23), # top_right
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(
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15,
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12,
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10,
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1,
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2,
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3,
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), # bottom_left
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(-2, -4, 21, 22, 23, 24, 26, 25), # bottom_right
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],
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}
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density_matrix_two_sites_vertical_rectangle: Definition = {
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"tensors": [
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["tensor", "tensor_conj", "T4"],
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["tensor", "tensor_conj", "T2"],
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"top_left",
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"top_right",
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"bottom_left",
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"bottom_right",
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],
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"network": [
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[
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(6, 19, 9, 11, 5), # tensor
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(8, 20, 9, 13, 7), # tensor_conj
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(18, 8, 6, 4), # T4
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],
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[
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(11, 22, 14, 16, 10), # tensor
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(13, 23, 14, 17, 12), # tensor_conj
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(16, 17, 21, 15), # T2
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],
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(-1, -3, 4, 5, 7, 1, 2, 3), # top_left
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(1, 2, 3, 15, 12, 10), # top_right
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(24, 25, 26, 18, 19, 20), # bottom_left
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(-2, -4, 21, 23, 22, 24, 25, 26), # bottom_right
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],
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}
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density_matrix_four_sites_top_left: Definition = {
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"tensors": [["tensor", "tensor_conj", "T4", "C1", "T1"]],
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"network": [

‎varipeps/expectation/__init__.py

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from . import one_site
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from . import two_sites
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from . import three_sites
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from . import four_sites
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from .model import Expectation_Model
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from .one_site import One_Site_Expectation_Value

‎varipeps/expectation/four_sites.py

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from functools import partial
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import jax.numpy as jnp
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from jax import jit
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from varipeps.peps import PEPS_Tensor
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from varipeps.contractions import apply_contraction_jitted
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from typing import Sequence, List, Tuple, Literal
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Corner_Literal = Literal["top-left", "top-right", "bottom-left", "bottom-right"]
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@partial(jit, static_argnums=(5,))
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def _four_sites_quadrat_workhorse(
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top_left: jnp.ndarray,
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top_right: jnp.ndarray,
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bottom_left: jnp.ndarray,
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bottom_right: jnp.ndarray,
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gates: Tuple[jnp.ndarray, ...],
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real_result: bool = False,
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) -> List[jnp.ndarray]:
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density_matrix = jnp.tensordot(top_left, top_right, ((5, 6, 7), (2, 3, 4)))
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density_matrix = jnp.tensordot(density_matrix, bottom_left, ((2, 3, 4), (5, 6, 7)))
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density_matrix = jnp.tensordot(
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density_matrix, bottom_right, ((4, 5, 6, 9, 10, 11), (2, 3, 4, 5, 6, 7))
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)
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density_matrix = density_matrix.transpose(0, 2, 4, 6, 1, 3, 5, 7)
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density_matrix = density_matrix.reshape(
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density_matrix.shape[0]
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* density_matrix.shape[1]
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* density_matrix.shape[2]
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* density_matrix.shape[3],
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density_matrix.shape[4]
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* density_matrix.shape[5]
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* density_matrix.shape[6]
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* density_matrix.shape[7],
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)
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norm = jnp.trace(density_matrix)
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if real_result:
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return [
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jnp.real(jnp.tensordot(density_matrix, g, ((0, 1), (0, 1))) / norm)
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for g in gates
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]
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else:
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return [
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jnp.tensordot(density_matrix, g, ((0, 1), (0, 1))) / norm for g in gates
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]
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def calc_four_sites_quadrat_multiple_gates(
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peps_tensors: Sequence[jnp.ndarray],
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peps_tensor_objs: Sequence[PEPS_Tensor],
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gates: Sequence[jnp.ndarray],
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) -> List[jnp.ndarray]:
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"""
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Calculate the four site expectation values for three as quadrat ordered
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PEPS tensor and their environment.
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The order of the PEPS sequence have to be
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[top-left, top-right, bottom-left, bottom-right].
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The gate is applied in the order [top-left, top-right, bottom-left, bottom-right].
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Args:
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peps_tensors (:term:`sequence` of :obj:`jax.numpy.ndarray`):
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The PEPS tensor arrays. Have to be the same objects as the tensor
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attribute of the `peps_tensor_obj` argument.
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peps_tensor_objs (:term:`sequence` of :obj:`~varipeps.peps.PEPS_Tensor`):
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PEPS tensor objects.
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gates (:term:`sequence` of :obj:`jax.numpy.ndarray`):
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Sequence with the gates which should be applied to the PEPS tensors.
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Gates are expected to be a matrix with first axis corresponding to
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the Hilbert space and the second axis corresponding to the dual room.
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Returns:
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:obj:`list` of :obj:`jax.numpy.ndarray`:
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List with the calculated expectation values of each gate.
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"""
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density_matrix_top_left = apply_contraction_jitted(
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"density_matrix_four_sites_top_left",
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[peps_tensors[0]],
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[peps_tensor_objs[0]],
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[],
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)
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density_matrix_top_right = apply_contraction_jitted(
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"density_matrix_four_sites_top_right",
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[peps_tensors[1]],
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[peps_tensor_objs[1]],
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[],
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)
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density_matrix_bottom_left = apply_contraction_jitted(
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"density_matrix_four_sites_bottom_left",
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[peps_tensors[2]],
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[peps_tensor_objs[2]],
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[],
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)
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density_matrix_bottom_right = apply_contraction_jitted(
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"density_matrix_four_sites_bottom_right",
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[peps_tensors[3]],
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[peps_tensor_objs[3]],
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[],
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)
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real_result = all(jnp.allclose(g, g.T.conj()) for g in gates)
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return _four_sites_quadrat_workhorse(
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density_matrix_top_left,
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density_matrix_top_right,
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density_matrix_bottom_left,
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density_matrix_bottom_right,
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tuple(gates),
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real_result,
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)

‎varipeps/expectation/spiral_helpers.py

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@@ -29,7 +29,8 @@ def apply_unitary(
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gate (:obj:`jax.numpy.ndarray`):
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The gate which should be updated with the unitary operator.
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delta_r (:obj:`jax.numpy.ndarray`):
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Vector for the spatial difference.
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Vector for the spatial difference. Can be a sequence if the spatial
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difference are different for the single indices.
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q (:term:`sequence` of :obj:`jax.numpy.ndarray`):
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Sequence with the relevant wavevector for the different indices of
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the gate.
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:obj:`jax.numpy.ndarray`:
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The updated gate with the unitary applied.
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"""
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if len(q) != len(apply_to_index):
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if isinstance(delta_r, jnp.ndarray):
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delta_r = (delta_r,) * len(apply_to_index)
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if len(q) != len(apply_to_index) or len(q) != len(delta_r):
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raise ValueError("Length mismatch!")
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working_gate = gate.reshape((phys_d,) * 2 * number_sites)
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for index, i in enumerate(apply_to_index):
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w_q = q[index]
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w_r = delta_r[index]
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if w_q.ndim == 0:
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w_q = jnp.array((w_q, w_q))
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else:
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raise ValueError("Unknown wavevector type!")
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# U = jsp.linalg.expm(1j * jnp.pi * jnp.dot(w_q, delta_r) * unitary_operator)
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U = jnp.exp(1j * jnp.pi * jnp.dot(w_q, delta_r) * unitary_operator_D)
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# U = jsp.linalg.expm(1j * jnp.pi * jnp.dot(w_q, w_r) * unitary_operator)
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U = jnp.exp(1j * jnp.pi * jnp.dot(w_q, w_r) * unitary_operator_D)
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U = jnp.dot(
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unitary_operator_sigma * U[jnp.newaxis, :], unitary_operator_sigma.T.conj()
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)

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