File size: 3,033 Bytes
6288873 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 | 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)
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