Source code for quimb.tensor.tensor_approx_spectral

"""Approximating spectral functions with tensor networks.
"""

import numpy as np
import random

import quimb as qu

from .tensor_gen import MPO_rand, MPO_zeros_like


[docs]def construct_lanczos_tridiag_MPO(A, K, v0=None, initial_bond_dim=None, beta_tol=1e-6, max_bond=None, seed=False, v0_opts=None, k_min=10): """ """ if initial_bond_dim is None: initial_bond_dim = 8 if max_bond is None: max_bond = 8 if v0 is None: if seed: # needs to be truly random so MPI processes don't overlap qu.seed_rand(random.SystemRandom().randint(0, 2**32 - 1)) V = MPO_rand(A.L, initial_bond_dim, phys_dim=A.phys_dim(), dtype=A.dtype) else: # normalize V = v0 / (v0.H @ v0)**0.5 Vm1 = MPO_zeros_like(V) alpha = np.zeros(K + 1) beta = np.zeros(K + 2) bsz = A.phys_dim()**A.L beta[1] = bsz # == sqrt(prod(A.shape)) compress_kws = {'max_bond': max_bond, 'method': 'svd'} for j in range(1, K + 1): Vt = A.apply(V, compress=True, **compress_kws) Vt.add_MPO(-beta[j] * Vm1, inplace=True, compress=True, **compress_kws) alpha[j] = (V.H @ Vt).real Vt.add_MPO(-alpha[j] * V, inplace=True, compress=True, **compress_kws) beta[j + 1] = (Vt.H @ Vt)**0.5 # check for convergence if abs(beta[j + 1]) < beta_tol: yield alpha[1:j + 1], beta[2:j + 2], beta[1]**2 / bsz break Vm1 = V.copy() V = Vt / beta[j + 1] if j >= k_min: yield (np.copy(alpha[1:j + 1]), np.copy(beta[2:j + 2]), np.copy(beta[1])**2 / bsz)