"""An example for purification MPS."""
# Copyright (C) TeNPy Developers, Apache license
from tenpy.algorithms.purification import PurificationApplyMPO, PurificationTEBD
from tenpy.models.tf_ising import TFIChain
from tenpy.networks.purification_mps import PurificationMPS
def imag_tebd(L=30, beta_max=3.0, dt=0.05, order=2, bc='finite'):
model_params = dict(L=L, J=1.0, g=1.2)
M = TFIChain(model_params)
psi = PurificationMPS.from_infiniteT(M.lat.mps_sites(), bc=bc)
options = {'trunc_params': {'chi_max': 100, 'svd_min': 1.0e-8}, 'order': order, 'dt': dt, 'N_steps': 1}
beta = 0.0
eng = PurificationTEBD(psi, M, options)
Szs = [psi.expectation_value('Sz')]
betas = [0.0]
while beta < beta_max:
beta += 2.0 * dt # factor of 2: |psi> ~= exp^{- dt H}, but rho = |psi><psi|
betas.append(beta)
eng.run_imaginary(dt) # cool down by dt
Szs.append(psi.expectation_value('Sz')) # and further measurements...
return {'beta': betas, 'Sz': Szs}
def imag_apply_mpo(L=30, beta_max=3.0, dt=0.05, order=2, bc='finite', approx='II'):
model_params = dict(L=L, J=1.0, g=1.2)
M = TFIChain(model_params)
psi = PurificationMPS.from_infiniteT(M.lat.mps_sites(), bc=bc)
options = {'trunc_params': {'chi_max': 100, 'svd_min': 1.0e-8}}
beta = 0.0
if order == 1:
Us = [M.H_MPO.make_U(-dt, approx)]
elif order == 2:
Us = [M.H_MPO.make_U(-d * dt, approx) for d in [0.5 + 0.5j, 0.5 - 0.5j]]
eng = PurificationApplyMPO(psi, Us[0], options)
Szs = [psi.expectation_value('Sz')]
betas = [0.0]
while beta < beta_max:
beta += 2.0 * dt # factor of 2: |psi> ~= exp^{- dt H}, but rho = |psi><psi|
betas.append(beta)
for U in Us:
eng.init_env(U) # reset environment, initialize new copy of psi
eng.run() # apply U to psi
Szs.append(psi.expectation_value('Sz')) # and further measurements...
return {'beta': betas, 'Sz': Szs}
if __name__ == '__main__':
import logging
logging.basicConfig(level=logging.INFO)
data_tebd = imag_tebd()
data_mpo = imag_apply_mpo()
import numpy as np
from matplotlib.pyplot import plt
plt.plot(data_mpo['beta'], np.sum(data_mpo['Sz'], axis=1), label='MPO')
plt.plot(data_tebd['beta'], np.sum(data_tebd['Sz'], axis=1), label='TEBD')
plt.xlabel(r'$\beta$')
plt.ylabel(r'total $S^z$')
plt.show()