"""Calculate the correlation length of the transverse field Ising model for various h_z.
This example uses DMRG to find the ground state of the transverse field Ising model when tuning
through the phase transition by changing the field `hz`. It uses
:meth:`~tenpy.networks.mps.MPS.correlation_length` to extract the correlation length of the ground
state, and plots it vs. hz in the end.
"""
# Copyright (C) TeNPy Developers, Apache license
import matplotlib.pyplot as plt
import numpy as np
from tenpy.algorithms import dmrg
from tenpy.models.spins import SpinChain
from tenpy.networks.mps import MPS
def run(Jzs):
L = 2
model_params = dict(L=L, Jx=1.0, Jy=1.0, Jz=Jzs[0], bc_MPS='infinite', conserve='Sz')
chi = 300
dmrg_params = {
'trunc_params': {'chi_max': chi, 'svd_min': 1.0e-10, 'trunc_cut': None},
'update_env': 20,
'start_env': 20,
'max_E_err': 0.0001,
'max_S_err': 0.0001,
'mixer': False,
}
M = SpinChain(model_params)
psi = MPS.from_product_state(
M.lat.mps_sites(), (['up', 'down'] * L)[:L], M.lat.bc_MPS, unit_cell_width=M.lat.mps_unit_cell_width
)
engine = dmrg.TwoSiteDMRGEngine(psi, M, dmrg_params)
np.set_printoptions(linewidth=120)
corr_length = []
for Jz in Jzs:
print('-' * 80)
print(f'{Jz=:.4f}')
print('-' * 80)
model_params['Jz'] = Jz
M = SpinChain(model_params)
engine.init_env(model=M) # (re)initialize DMRG environment with new model
# this uses the result from the previous DMRG as first initial guess
engine.run()
# psi is modified by engine.run() and now represents the ground state for the current `Jz`.
corr_length.append(psi.correlation_length(tol_ev0=1.0e-3))
print('corr. length', corr_length[-1])
print('<Sz>', psi.expectation_value('Sz'))
dmrg_params['start_env'] = 0 # (some of) the parameters are read out again
corr_length = np.array(corr_length)
results = {
'model_params': model_params,
'dmrg_params': dmrg_params,
'Jzs': Jzs,
'corr_length': corr_length,
'eval_transfermatrix': np.exp(-1.0 / corr_length),
}
return results
def plot(results, filename):
corr_length = results['corr_length']
Jzs = results['Jzs']
plt.plot(Jzs, np.exp(-1.0 / corr_length))
plt.xlabel(r'$J_z/J_x$')
plt.ylabel(r'$t = \exp(-\frac{1}{\xi})$')
plt.savefig(filename)
print('saved to ' + filename)
if __name__ == '__main__':
filename = 'xxz_corrlength.pkl'
import os.path
import pickle
if not os.path.exists(filename):
results = run(list(np.arange(4.0, 1.5, -0.25)) + list(np.arange(1.5, 0.8, -0.05)))
with open(filename, 'wb') as f:
pickle.dump(results, f)
else:
print('just load the data')
with open(filename, 'rb') as f:
results = pickle.load(f)
plot(results, filename[:-4] + '.pdf')