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Sampling of Purification MPS

This notebook demonstrates how to sample basis states from a purification MPS to evaluate expectation values. While we demonstrate this for magnetization, a sum of local quantities \(\langle Z_i \rangle\), sampling could be useful to stochastically evaluate non-local expectation values where contraction of the tensor network for exact evaluation is expensive. To demonstrate this functionality, we find the purification of the thermal density matrix \(\rho \propto e^{-\beta H}\) for the transverse field Ising model as a function of inverse temperature \(\beta\). We represent the density matrix as a purified pure state \(|\psi \rangle\) on an enlarged Hilbert space $:nbsphinx-math:mathcal{H}_p \otimes `:nbsphinx-math:mathcal{H}`_a $ such that \(\rho = \mathrm{Tr}_a |\psi \rangle \langle \psi |\).

The algorithm from sampling purification MPS is a simple extension of that for sampling MPS, explained in detail in the following two papers: 1. https://arxiv.org/abs/1002.1305 2. https://arxiv.org/abs/1201.3974

import numpy as np
import matplotlib.pyplot as plt
import sys
from time import time
import logging
logging.basicConfig(level=logging.INFO)

import tenpy
from tenpy.models.tf_ising import TFIChain
from tenpy.networks.purification_mps import PurificationMPS
from tenpy.algorithms.purification import PurificationTEBD, PurificationApplyMPO

Run purification TEBD and measure magnetization on each site, both by contracting the tensor network (really by using orthogonality conditions to avoid most of the work) or sampling.

def imag_tebd(L=30, beta_max=3., dt=0.05, order=2, bc="finite", num_samples=1000, chi_max=100, sample_all=True):
    model_params = dict(L=L, J=1., g=1.2)
    M = TFIChain(model_params)
    psi = PurificationMPS.from_infiniteT(M.lat.mps_sites(), bc=bc)
    options = {
        'trunc_params': {
            'chi_max': chi_max,
            'svd_min': 1.e-8
        },
        'order': order,
        'dt': dt,
        'N_steps': 1
    }
    beta = 0.
    eng = PurificationTEBD(psi, M, options)
    Szs = [psi.expectation_value("Sz")]
    Szs_sample_sq, Szs_sample_nsq, sampling_time_sq, sampling_time_nsq = [], [], [], []
    if sample_all:
        sample_data = sample_purification(psi, num_samples)
        Szs_sample_sq.append(sample_data[0][0])
        Szs_sample_nsq.append(sample_data[1][0])
        sampling_time_sq.append(sample_data[0][2])
        sampling_time_nsq.append(sample_data[1][2])
    betas = [0.]
    psis = [psi.copy()]
    while beta < beta_max:
        beta += 2. * 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...
        if sample_all or np.isclose(beta, beta_max):
            print(psi.chi)
            sample_data = sample_purification(psi, num_samples)
            Szs_sample_sq.append(sample_data[0][0])
            Szs_sample_nsq.append(sample_data[1][0])
            sampling_time_sq.append(sample_data[0][2])
            sampling_time_nsq.append(sample_data[1][2])
        psis.append(psi.copy())
    return {'beta': betas, 'Sz': Szs, 'Sz_sample_sq': Szs_sample_sq, 'Sz_sample_nsq': Szs_sample_nsq,
            'time_sq': sampling_time_sq, 'time_nsq': sampling_time_nsq,
            'psi': psis}

Below we repeatedly sample a purification MPS to determine the magnetization. Depending on the value of sample_q, we either sample the ancilla leg (True) or contract over it (False). The first is cheaper than the latter, with a cost of \(\mathcal{}(\chi^2)\) compared to \(\mathcal{}(\chi^3)\).

def sample_purification(psi, num_samples):
    data = []
    for sample_q in [True, False]:
        magnetization = []
        start_time = time()
        for i in range(num_samples):
            sigmas, total_prob = psi.sample_measurements(sample_q, complex_amplitude=False)
            magnetization.append(np.array(sigmas) - 1/2) # 1 index corresponds to spin up I guess
        sample_time = time() - start_time
        magnetization = np.row_stack(magnetization)
        data.append((magnetization.mean(axis=0), magnetization, sample_time / num_samples))
    return data

Average magnetization as a function of \(\beta\)

# note: this cell is skipped in pytest
data_tebd = imag_tebd(L=30, beta_max=3.0, num_samples=50)

plt.plot(data_tebd['beta'], np.sum(data_tebd['Sz'], axis=1), label='TEBD')
plt.plot(data_tebd['beta'], np.sum(data_tebd['Sz_sample_sq'], axis=1), '.', label='TEBD; sampling q')
plt.plot(data_tebd['beta'], np.sum(data_tebd['Sz_sample_nsq'], axis=1), '.', label='TEBD; tracing q')

plt.legend()
plt.xlabel(r'$\beta$')
plt.ylabel(r'total $S^z$')
plt.show()

INFO:tenpy.tools.params:TFIChain: reading 'L'=30
INFO:tenpy.tools.params:TFIChain: reading 'J'=1.0
INFO:tenpy.tools.params:TFIChain: reading 'g'=1.2
INFO:tenpy.tools.params:PurificationTEBD: subconfig 'trunc_params'=Config(<2 options>, 'trunc_params')
INFO:tenpy.tools.params:PurificationTEBD: reading 'dt'=0.05
INFO:tenpy.algorithms.tebd:Calculate U for {'order': 2, 'delta_t': 0.05, 'type_evo': 'imag', 'E_offset': None, 'tau': -0.05j}
INFO:tenpy.tools.params:trunc_params: reading 'chi_max'=100
INFO:tenpy.tools.params:trunc_params: reading 'svd_min'=1e-08
INFO:tenpy.algorithms.purification:--> beta=0.050000, E_bond=-0.2460708907, max(S)=0.0172500676

[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]

INFO:tenpy.algorithms.purification:--> beta=0.100000, E_bond=-0.4756494810, max(S)=0.0532230133

[4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4]

INFO:tenpy.algorithms.purification:--> beta=0.150000, E_bond=-0.6767971387, max(S)=0.0967049734

[4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4]

INFO:tenpy.algorithms.purification:--> beta=0.200000, E_bond=-0.8441540463, max(S)=0.1411322525

[4, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4]

INFO:tenpy.algorithms.purification:--> beta=0.250000, E_bond=-0.9781014310, max(S)=0.1827168026

[4, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 4]

/Users/jakobunfried/tenpy/development/tenpy/tools/params.py:232: UserWarning: unused options for config PurificationTEBD:
['N_steps', 'order']
  warnings.warn(msg.format(keys=sorted(unused), name=self.name))
INFO:tenpy.algorithms.purification:--> beta=0.300000, E_bond=-1.0825193832, max(S)=0.2197692357

[4, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 4]

INFO:tenpy.algorithms.purification:--> beta=0.350000, E_bond=-1.1626430338, max(S)=0.2518978714

[4, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 4]

INFO:tenpy.algorithms.purification:--> beta=0.400000, E_bond=-1.2236704021, max(S)=0.2793931954

[4, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 4]

INFO:tenpy.algorithms.purification:--> beta=0.450000, E_bond=-1.2701012984, max(S)=0.3028286284

[4, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 4]

INFO:tenpy.algorithms.purification:--> beta=0.500000, E_bond=-1.3055507972, max(S)=0.3228394786

[4, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 4]

INFO:tenpy.algorithms.purification:--> beta=0.550000, E_bond=-1.3328003341, max(S)=0.3400180953

[4, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 12, 4]

INFO:tenpy.algorithms.purification:--> beta=0.600000, E_bond=-1.3539370350, max(S)=0.3548744861

[4, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 12, 4]

INFO:tenpy.algorithms.purification:--> beta=0.650000, E_bond=-1.3705056888, max(S)=0.3678296985

[4, 12, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 12, 4]

INFO:tenpy.algorithms.purification:--> beta=0.700000, E_bond=-1.3836424298, max(S)=0.3792235056

[4, 13, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 13, 4]

INFO:tenpy.algorithms.purification:--> beta=0.750000, E_bond=-1.3941816805, max(S)=0.3893269224

[4, 13, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 13, 4]

INFO:tenpy.algorithms.purification:--> beta=0.800000, E_bond=-1.4027375341, max(S)=0.3983551258

[4, 14, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 16, 16, 14, 4]

INFO:tenpy.algorithms.purification:--> beta=0.850000, E_bond=-1.4097639705, max(S)=0.4064789719

[4, 14, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 14, 4]

INFO:tenpy.algorithms.purification:--> beta=0.900000, E_bond=-1.4155987119, max(S)=0.4138345776

[4, 14, 17, 17, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 17, 17, 14, 4]

INFO:tenpy.algorithms.purification:--> beta=0.950000, E_bond=-1.4204948992, max(S)=0.4205309982

[4, 15, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 15, 4]

INFO:tenpy.algorithms.purification:--> beta=1.000000, E_bond=-1.4246438890, max(S)=0.4266562471

[4, 15, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 15, 4]

INFO:tenpy.algorithms.purification:--> beta=1.050000, E_bond=-1.4281916571, max(S)=0.4322819578

[4, 16, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 15, 4]

INFO:tenpy.algorithms.purification:--> beta=1.100000, E_bond=-1.4312506260, max(S)=0.4374669712

[4, 16, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.150000, E_bond=-1.4339082234, max(S)=0.4422600875

[4, 16, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.200000, E_bond=-1.4362331074, max(S)=0.4467021777

[4, 16, 22, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 22, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.250000, E_bond=-1.4382797204, max(S)=0.4508278067

[4, 16, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.300000, E_bond=-1.4400916437, max(S)=0.4546664848

[4, 16, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.350000, E_bond=-1.4417040858, max(S)=0.4582436383

[4, 16, 23, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 23, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.400000, E_bond=-1.4431457429, max(S)=0.4615813653

[4, 16, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.450000, E_bond=-1.4444402010, max(S)=0.4646990279

[4, 16, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.500000, E_bond=-1.4456070009, max(S)=0.4676137204

[4, 16, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 16, 4]

Do a quick sanity check, if the above curves actually agree. Use smaller \(L\) and \(\beta\), such that we can use this as part of the github actions

data = imag_tebd(L=20, beta_max=1.0, num_samples=50)

diffs_sampling = np.sum(data['Sz'], axis=1) - np.sum(data['Sz_sample_sq'], axis=1)
mse_sampling = np.sum(np.abs(diffs_sampling) ** 2 ) / len(diffs_sampling)
diffs_tracing = np.sum(data['Sz'], axis=1) - np.sum(data['Sz_sample_nsq'], axis=1)
mse_tracing = np.sum(np.abs(diffs_tracing) ** 2 ) / len(diffs_tracing)
print(mse_sampling)
print(mse_tracing)
assert mse_sampling < 1
assert mse_tracing < 1

INFO:tenpy.tools.params:TFIChain: reading 'L'=20
INFO:tenpy.tools.params:TFIChain: reading 'J'=1.0
INFO:tenpy.tools.params:TFIChain: reading 'g'=1.2
INFO:tenpy.tools.params:PurificationTEBD: subconfig 'trunc_params'=Config(<2 options>, 'trunc_params')
INFO:tenpy.tools.params:PurificationTEBD: reading 'dt'=0.05
INFO:tenpy.algorithms.tebd:Calculate U for {'order': 2, 'delta_t': 0.05, 'type_evo': 'imag', 'E_offset': None, 'tau': -0.05j}
INFO:tenpy.tools.params:trunc_params: reading 'chi_max'=100
INFO:tenpy.tools.params:trunc_params: reading 'svd_min'=1e-08
INFO:tenpy.algorithms.purification:--> beta=0.050000, E_bond=-0.2486712411, max(S)=0.0172500676

[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]

INFO:tenpy.algorithms.purification:--> beta=0.100000, E_bond=-0.4807745902, max(S)=0.0532230133

[4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4]

INFO:tenpy.algorithms.purification:--> beta=0.150000, E_bond=-0.6842967410, max(S)=0.0967049734

[4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4]

INFO:tenpy.algorithms.purification:--> beta=0.200000, E_bond=-0.8538132645, max(S)=0.1411322525

[4, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4]

INFO:tenpy.algorithms.purification:--> beta=0.250000, E_bond=-0.9896631609, max(S)=0.1827168026

[4, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 4]

INFO:tenpy.algorithms.purification:--> beta=0.300000, E_bond=-1.0957122376, max(S)=0.2197692357

[4, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 4]

INFO:tenpy.algorithms.purification:--> beta=0.350000, E_bond=-1.1772055723, max(S)=0.2518978714

[4, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 4]

INFO:tenpy.algorithms.purification:--> beta=0.400000, E_bond=-1.2393667416, max(S)=0.2793931954

[4, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 4]

INFO:tenpy.algorithms.purification:--> beta=0.450000, E_bond=-1.2867281260, max(S)=0.3028286284

[4, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 4]

INFO:tenpy.algorithms.purification:--> beta=0.500000, E_bond=-1.3229382086, max(S)=0.3228394786

[4, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 4]

INFO:tenpy.algorithms.purification:--> beta=0.550000, E_bond=-1.3508091638, max(S)=0.3400180953

[4, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 12, 4]
0.12407017068350712
0.10186772056872069

Now we look at sampling time as a function of \(\beta\). We expect this to be independent of \(\beta\) and only dependent on \(\chi\).

plt.plot(data_tebd['beta'], data_tebd['time_sq'], '.', label='TEBD; sampling q')
plt.plot(data_tebd['beta'], data_tebd['time_nsq'], '.', label='TEBD; tracing q')

plt.legend()
plt.xlabel(r'$\beta$')
plt.ylabel(r'Sampling Time')
plt.show()

/Users/jakobunfried/tenpy/development/tenpy/tools/params.py:232: UserWarning: unused options for config PurificationTEBD:
['N_steps', 'order']
  warnings.warn(msg.format(keys=sorted(unused), name=self.name))

Sampling time dependence on chi

datas_tebd = {}
for chi in [2, 4, 8, 12, 16, 20, 24]:
    datas_tebd[chi] = imag_tebd(L=30, beta_max=3.0, num_samples=50, chi_max=chi, sample_all=False)

INFO:tenpy.tools.params:TFIChain: reading 'L'=30
INFO:tenpy.tools.params:TFIChain: reading 'J'=1.0
INFO:tenpy.tools.params:TFIChain: reading 'g'=1.2
INFO:tenpy.tools.params:PurificationTEBD: subconfig 'trunc_params'=Config(<2 options>, 'trunc_params')
INFO:tenpy.tools.params:PurificationTEBD: reading 'dt'=0.05
INFO:tenpy.algorithms.tebd:Calculate U for {'order': 2, 'delta_t': 0.05, 'type_evo': 'imag', 'E_offset': None, 'tau': -0.05j}
INFO:tenpy.tools.params:trunc_params: reading 'chi_max'=2
INFO:tenpy.tools.params:trunc_params: reading 'svd_min'=1e-08
INFO:tenpy.algorithms.purification:--> beta=0.050000, E_bond=-0.2460704684, max(S)=0.0172499542
INFO:tenpy.algorithms.purification:--> beta=0.100000, E_bond=-0.4756295855, max(S)=0.0532187236
INFO:tenpy.algorithms.purification:--> beta=0.150000, E_bond=-0.6766525889, max(S)=0.0966746449
INFO:tenpy.algorithms.purification:--> beta=0.200000, E_bond=-0.8436355045, max(S)=0.1410008935
INFO:tenpy.algorithms.purification:--> beta=0.250000, E_bond=-0.9768282106, max(S)=0.1823408159
INFO:tenpy.algorithms.purification:--> beta=0.300000, E_bond=-1.0800497086, max(S)=0.2189349620
INFO:tenpy.algorithms.purification:--> beta=0.350000, E_bond=-1.1585539424, max(S)=0.2503366410
INFO:tenpy.algorithms.purification:--> beta=0.400000, E_bond=-1.2176145022, max(S)=0.2768028450
INFO:tenpy.algorithms.purification:--> beta=0.450000, E_bond=-1.2618331065, max(S)=0.2988946378
INFO:tenpy.algorithms.purification:--> beta=0.500000, E_bond=-1.2949295484, max(S)=0.3172523022
INFO:tenpy.algorithms.purification:--> beta=0.550000, E_bond=-1.3197791128, max(S)=0.3324856739
INFO:tenpy.algorithms.purification:--> beta=0.600000, E_bond=-1.3385459894, max(S)=0.3451301838
INFO:tenpy.algorithms.purification:--> beta=0.650000, E_bond=-1.3528341236, max(S)=0.3556364310
INFO:tenpy.algorithms.purification:--> beta=0.700000, E_bond=-1.3638222698, max(S)=0.3643749599
INFO:tenpy.algorithms.purification:--> beta=0.750000, E_bond=-1.3723733559, max(S)=0.3716467144
INFO:tenpy.algorithms.purification:--> beta=0.800000, E_bond=-1.3791185376, max(S)=0.3776946110
INFO:tenpy.algorithms.purification:--> beta=0.850000, E_bond=-1.3845199431, max(S)=0.3827142764
INFO:tenpy.algorithms.purification:--> beta=0.900000, E_bond=-1.3889167423, max(S)=0.3868632701
INFO:tenpy.algorithms.purification:--> beta=0.950000, E_bond=-1.3925586707, max(S)=0.3902687015
INFO:tenpy.algorithms.purification:--> beta=1.000000, E_bond=-1.3956303182, max(S)=0.3930333886
INFO:tenpy.algorithms.purification:--> beta=1.050000, E_bond=-1.3982687029, max(S)=0.3952407804
INFO:tenpy.algorithms.purification:--> beta=1.100000, E_bond=-1.4005759943, max(S)=0.3969588716
INFO:tenpy.algorithms.purification:--> beta=1.150000, E_bond=-1.4026287395, max(S)=0.3982433085
INFO:tenpy.algorithms.purification:--> beta=1.200000, E_bond=-1.4044845733, max(S)=0.3991398545
INFO:tenpy.algorithms.purification:--> beta=1.250000, E_bond=-1.4061871111, max(S)=0.3996863519
INFO:tenpy.algorithms.purification:--> beta=1.300000, E_bond=-1.4077695311, max(S)=0.3999142853
INFO:tenpy.algorithms.purification:--> beta=1.350000, E_bond=-1.4092572046, max(S)=0.3998500337
INFO:tenpy.algorithms.purification:--> beta=1.400000, E_bond=-1.4106696360, max(S)=0.3995158765
INFO:tenpy.algorithms.purification:--> beta=1.450000, E_bond=-1.4120218982, max(S)=0.3989308037
INFO:tenpy.algorithms.purification:--> beta=1.500000, E_bond=-1.4133256987, max(S)=0.3981111736

[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]

INFO:tenpy.tools.params:TFIChain: reading 'L'=30
INFO:tenpy.tools.params:TFIChain: reading 'J'=1.0
INFO:tenpy.tools.params:TFIChain: reading 'g'=1.2
INFO:tenpy.tools.params:PurificationTEBD: subconfig 'trunc_params'=Config(<2 options>, 'trunc_params')
INFO:tenpy.tools.params:PurificationTEBD: reading 'dt'=0.05
INFO:tenpy.algorithms.tebd:Calculate U for {'order': 2, 'delta_t': 0.05, 'type_evo': 'imag', 'E_offset': None, 'tau': -0.05j}
INFO:tenpy.tools.params:trunc_params: reading 'chi_max'=4
INFO:tenpy.tools.params:trunc_params: reading 'svd_min'=1e-08
INFO:tenpy.algorithms.purification:--> beta=0.050000, E_bond=-0.2460708907, max(S)=0.0172500676
INFO:tenpy.algorithms.purification:--> beta=0.100000, E_bond=-0.4756494809, max(S)=0.0532230133
INFO:tenpy.algorithms.purification:--> beta=0.150000, E_bond=-0.6767971354, max(S)=0.0967049716
INFO:tenpy.algorithms.purification:--> beta=0.200000, E_bond=-0.8441540073, max(S)=0.1411322267
INFO:tenpy.algorithms.purification:--> beta=0.250000, E_bond=-0.9781012074, max(S)=0.1827166245
INFO:tenpy.algorithms.purification:--> beta=0.300000, E_bond=-1.0825185679, max(S)=0.2197684742
INFO:tenpy.algorithms.purification:--> beta=0.350000, E_bond=-1.1626408176, max(S)=0.2518954752
INFO:tenpy.algorithms.purification:--> beta=0.400000, E_bond=-1.2236654898, max(S)=0.2793871022
INFO:tenpy.algorithms.purification:--> beta=0.450000, E_bond=-1.2700919103, max(S)=0.3028153664
INFO:tenpy.algorithms.purification:--> beta=0.500000, E_bond=-1.3055347414, max(S)=0.3228138181
INFO:tenpy.algorithms.purification:--> beta=0.550000, E_bond=-1.3327751177, max(S)=0.3399727867
INFO:tenpy.algorithms.purification:--> beta=0.600000, E_bond=-1.3538999884, max(S)=0.3548001033
INFO:tenpy.algorithms.purification:--> beta=0.650000, E_bond=-1.3704540845, max(S)=0.3677145909
INFO:tenpy.algorithms.purification:--> beta=0.700000, E_bond=-1.3835735866, max(S)=0.3790538537
INFO:tenpy.algorithms.purification:--> beta=0.750000, E_bond=-1.3940930523, max(S)=0.3890868855
INFO:tenpy.algorithms.purification:--> beta=0.800000, E_bond=-1.4026267814, max(S)=0.3980270661
INFO:tenpy.algorithms.purification:--> beta=0.850000, E_bond=-1.4096290161, max(S)=0.4060437379
INFO:tenpy.algorithms.purification:--> beta=0.900000, E_bond=-1.4154377814, max(S)=0.4132718286
INFO:tenpy.algorithms.purification:--> beta=0.950000, E_bond=-1.4203065474, max(S)=0.4198195522
INFO:tenpy.algorithms.purification:--> beta=1.000000, E_bond=-1.4244270136, max(S)=0.4257744365
INFO:tenpy.algorithms.purification:--> beta=1.050000, E_bond=-1.4279455007, max(S)=0.4312079787
INFO:tenpy.algorithms.purification:--> beta=1.100000, E_bond=-1.4309747678, max(S)=0.4361792156
INFO:tenpy.algorithms.purification:--> beta=1.150000, E_bond=-1.4336025622, max(S)=0.4407374495
INFO:tenpy.algorithms.purification:--> beta=1.200000, E_bond=-1.4358978383, max(S)=0.4449243276
INFO:tenpy.algorithms.purification:--> beta=1.250000, E_bond=-1.4379153060, max(S)=0.4487754294
INFO:tenpy.algorithms.purification:--> beta=1.300000, E_bond=-1.4396987828, max(S)=0.4523214816
INFO:tenpy.algorithms.purification:--> beta=1.350000, E_bond=-1.4412836798, max(S)=0.4555892900
INFO:tenpy.algorithms.purification:--> beta=1.400000, E_bond=-1.4426988619, max(S)=0.4586024594
INFO:tenpy.algorithms.purification:--> beta=1.450000, E_bond=-1.4439680509, max(S)=0.4613819516
INFO:tenpy.algorithms.purification:--> beta=1.500000, E_bond=-1.4451108922, max(S)=0.4639465212

[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]

INFO:tenpy.tools.params:TFIChain: reading 'L'=30
INFO:tenpy.tools.params:TFIChain: reading 'J'=1.0
INFO:tenpy.tools.params:TFIChain: reading 'g'=1.2
INFO:tenpy.tools.params:PurificationTEBD: subconfig 'trunc_params'=Config(<2 options>, 'trunc_params')
INFO:tenpy.tools.params:PurificationTEBD: reading 'dt'=0.05
INFO:tenpy.algorithms.tebd:Calculate U for {'order': 2, 'delta_t': 0.05, 'type_evo': 'imag', 'E_offset': None, 'tau': -0.05j}
INFO:tenpy.tools.params:trunc_params: reading 'chi_max'=8
INFO:tenpy.tools.params:trunc_params: reading 'svd_min'=1e-08
INFO:tenpy.algorithms.purification:--> beta=0.050000, E_bond=-0.2460708907, max(S)=0.0172500676
INFO:tenpy.algorithms.purification:--> beta=0.100000, E_bond=-0.4756494810, max(S)=0.0532230133
INFO:tenpy.algorithms.purification:--> beta=0.150000, E_bond=-0.6767971387, max(S)=0.0967049734
INFO:tenpy.algorithms.purification:--> beta=0.200000, E_bond=-0.8441540463, max(S)=0.1411322525
INFO:tenpy.algorithms.purification:--> beta=0.250000, E_bond=-0.9781014308, max(S)=0.1827168024
INFO:tenpy.algorithms.purification:--> beta=0.300000, E_bond=-1.0825193810, max(S)=0.2197692330
INFO:tenpy.algorithms.purification:--> beta=0.350000, E_bond=-1.1626430248, max(S)=0.2518978586
INFO:tenpy.algorithms.purification:--> beta=0.400000, E_bond=-1.2236703781, max(S)=0.2793931551
INFO:tenpy.algorithms.purification:--> beta=0.450000, E_bond=-1.2701012469, max(S)=0.3028285287
INFO:tenpy.algorithms.purification:--> beta=0.500000, E_bond=-1.3055507023, max(S)=0.3228392682
INFO:tenpy.algorithms.purification:--> beta=0.550000, E_bond=-1.3328001762, max(S)=0.3400176995
INFO:tenpy.algorithms.purification:--> beta=0.600000, E_bond=-1.3539367912, max(S)=0.3548738039
INFO:tenpy.algorithms.purification:--> beta=0.650000, E_bond=-1.3705053320, max(S)=0.3678285994
INFO:tenpy.algorithms.purification:--> beta=0.700000, E_bond=-1.3836419271, max(S)=0.3792218274
INFO:tenpy.algorithms.purification:--> beta=0.750000, E_bond=-1.3941809928, max(S)=0.3893244680
INFO:tenpy.algorithms.purification:--> beta=0.800000, E_bond=-1.4027366149, max(S)=0.3983516592
INFO:tenpy.algorithms.purification:--> beta=0.850000, E_bond=-1.4097627652, max(S)=0.4064742140
INFO:tenpy.algorithms.purification:--> beta=0.900000, E_bond=-1.4155971581, max(S)=0.4138282015
INFO:tenpy.algorithms.purification:--> beta=0.950000, E_bond=-1.4204929266, max(S)=0.4205226238
INFO:tenpy.algorithms.purification:--> beta=1.000000, E_bond=-1.4246414203, max(S)=0.4266454364
INFO:tenpy.algorithms.purification:--> beta=1.050000, E_bond=-1.4281886096, max(S)=0.4322682107
INFO:tenpy.algorithms.purification:--> beta=1.100000, E_bond=-1.4312469127, max(S)=0.4374497211
INFO:tenpy.algorithms.purification:--> beta=1.150000, E_bond=-1.4339037547, max(S)=0.4422386982
INFO:tenpy.algorithms.purification:--> beta=1.200000, E_bond=-1.4362277928, max(S)=0.4466759411
INFO:tenpy.algorithms.purification:--> beta=1.250000, E_bond=-1.4382734699, max(S)=0.4507959412
INFO:tenpy.algorithms.purification:--> beta=1.300000, E_bond=-1.4400843695, max(S)=0.4546281348
INFO:tenpy.algorithms.purification:--> beta=1.350000, E_bond=-1.4416957037, max(S)=0.4581978748
INFO:tenpy.algorithms.purification:--> beta=1.400000, E_bond=-1.4431361732, max(S)=0.4615271866
INFO:tenpy.algorithms.purification:--> beta=1.450000, E_bond=-1.4444293699, max(S)=0.4646353619
INFO:tenpy.algorithms.purification:--> beta=1.500000, E_bond=-1.4455948410, max(S)=0.4675394269

[4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4]

INFO:tenpy.tools.params:TFIChain: reading 'L'=30
INFO:tenpy.tools.params:TFIChain: reading 'J'=1.0
INFO:tenpy.tools.params:TFIChain: reading 'g'=1.2
INFO:tenpy.tools.params:PurificationTEBD: subconfig 'trunc_params'=Config(<2 options>, 'trunc_params')
INFO:tenpy.tools.params:PurificationTEBD: reading 'dt'=0.05
INFO:tenpy.algorithms.tebd:Calculate U for {'order': 2, 'delta_t': 0.05, 'type_evo': 'imag', 'E_offset': None, 'tau': -0.05j}
INFO:tenpy.tools.params:trunc_params: reading 'chi_max'=12
INFO:tenpy.tools.params:trunc_params: reading 'svd_min'=1e-08
INFO:tenpy.algorithms.purification:--> beta=0.050000, E_bond=-0.2460708907, max(S)=0.0172500676
INFO:tenpy.algorithms.purification:--> beta=0.100000, E_bond=-0.4756494810, max(S)=0.0532230133
INFO:tenpy.algorithms.purification:--> beta=0.150000, E_bond=-0.6767971387, max(S)=0.0967049734
INFO:tenpy.algorithms.purification:--> beta=0.200000, E_bond=-0.8441540463, max(S)=0.1411322525
INFO:tenpy.algorithms.purification:--> beta=0.250000, E_bond=-0.9781014310, max(S)=0.1827168026
INFO:tenpy.algorithms.purification:--> beta=0.300000, E_bond=-1.0825193832, max(S)=0.2197692357
INFO:tenpy.algorithms.purification:--> beta=0.350000, E_bond=-1.1626430338, max(S)=0.2518978714
INFO:tenpy.algorithms.purification:--> beta=0.400000, E_bond=-1.2236704021, max(S)=0.2793931954
INFO:tenpy.algorithms.purification:--> beta=0.450000, E_bond=-1.2701012984, max(S)=0.3028286284
INFO:tenpy.algorithms.purification:--> beta=0.500000, E_bond=-1.3055507972, max(S)=0.3228394786
INFO:tenpy.algorithms.purification:--> beta=0.550000, E_bond=-1.3328003341, max(S)=0.3400180953
INFO:tenpy.algorithms.purification:--> beta=0.600000, E_bond=-1.3539370349, max(S)=0.3548744860
INFO:tenpy.algorithms.purification:--> beta=0.650000, E_bond=-1.3705056887, max(S)=0.3678296982
INFO:tenpy.algorithms.purification:--> beta=0.700000, E_bond=-1.3836424292, max(S)=0.3792235047
INFO:tenpy.algorithms.purification:--> beta=0.750000, E_bond=-1.3941816790, max(S)=0.3893269208
INFO:tenpy.algorithms.purification:--> beta=0.800000, E_bond=-1.4027375311, max(S)=0.3983551228
INFO:tenpy.algorithms.purification:--> beta=0.850000, E_bond=-1.4097639652, max(S)=0.4064789662
INFO:tenpy.algorithms.purification:--> beta=0.900000, E_bond=-1.4155987036, max(S)=0.4138345672
INFO:tenpy.algorithms.purification:--> beta=0.950000, E_bond=-1.4204948869, max(S)=0.4205309799
INFO:tenpy.algorithms.purification:--> beta=1.000000, E_bond=-1.4246438716, max(S)=0.4266562160
INFO:tenpy.algorithms.purification:--> beta=1.050000, E_bond=-1.4281916334, max(S)=0.4322819071
INFO:tenpy.algorithms.purification:--> beta=1.100000, E_bond=-1.4312505947, max(S)=0.4374668917
INFO:tenpy.algorithms.purification:--> beta=1.150000, E_bond=-1.4339081830, max(S)=0.4422599668
INFO:tenpy.algorithms.purification:--> beta=1.200000, E_bond=-1.4362330562, max(S)=0.4467019998
INFO:tenpy.algorithms.purification:--> beta=1.250000, E_bond=-1.4382796566, max(S)=0.4508275513
INFO:tenpy.algorithms.purification:--> beta=1.300000, E_bond=-1.4400915653, max(S)=0.4546661269
INFO:tenpy.algorithms.purification:--> beta=1.350000, E_bond=-1.4417039908, max(S)=0.4582431474
INFO:tenpy.algorithms.purification:--> beta=1.400000, E_bond=-1.4431456291, max(S)=0.4615807051
INFO:tenpy.algorithms.purification:--> beta=1.450000, E_bond=-1.4444400661, max(S)=0.4646981557
INFO:tenpy.algorithms.purification:--> beta=1.500000, E_bond=-1.4456068426, max(S)=0.4676125866

[4, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 4]

INFO:tenpy.tools.params:TFIChain: reading 'L'=30
INFO:tenpy.tools.params:TFIChain: reading 'J'=1.0
INFO:tenpy.tools.params:TFIChain: reading 'g'=1.2
INFO:tenpy.tools.params:PurificationTEBD: subconfig 'trunc_params'=Config(<2 options>, 'trunc_params')
INFO:tenpy.tools.params:PurificationTEBD: reading 'dt'=0.05
INFO:tenpy.algorithms.tebd:Calculate U for {'order': 2, 'delta_t': 0.05, 'type_evo': 'imag', 'E_offset': None, 'tau': -0.05j}
INFO:tenpy.tools.params:trunc_params: reading 'chi_max'=16
INFO:tenpy.tools.params:trunc_params: reading 'svd_min'=1e-08
INFO:tenpy.algorithms.purification:--> beta=0.050000, E_bond=-0.2460708907, max(S)=0.0172500676
INFO:tenpy.algorithms.purification:--> beta=0.100000, E_bond=-0.4756494810, max(S)=0.0532230133
INFO:tenpy.algorithms.purification:--> beta=0.150000, E_bond=-0.6767971387, max(S)=0.0967049734
INFO:tenpy.algorithms.purification:--> beta=0.200000, E_bond=-0.8441540463, max(S)=0.1411322525
INFO:tenpy.algorithms.purification:--> beta=0.250000, E_bond=-0.9781014310, max(S)=0.1827168026
INFO:tenpy.algorithms.purification:--> beta=0.300000, E_bond=-1.0825193832, max(S)=0.2197692357
INFO:tenpy.algorithms.purification:--> beta=0.350000, E_bond=-1.1626430338, max(S)=0.2518978714
INFO:tenpy.algorithms.purification:--> beta=0.400000, E_bond=-1.2236704021, max(S)=0.2793931954
INFO:tenpy.algorithms.purification:--> beta=0.450000, E_bond=-1.2701012984, max(S)=0.3028286284
INFO:tenpy.algorithms.purification:--> beta=0.500000, E_bond=-1.3055507972, max(S)=0.3228394786
INFO:tenpy.algorithms.purification:--> beta=0.550000, E_bond=-1.3328003341, max(S)=0.3400180953
INFO:tenpy.algorithms.purification:--> beta=0.600000, E_bond=-1.3539370350, max(S)=0.3548744861
INFO:tenpy.algorithms.purification:--> beta=0.650000, E_bond=-1.3705056888, max(S)=0.3678296985
INFO:tenpy.algorithms.purification:--> beta=0.700000, E_bond=-1.3836424298, max(S)=0.3792235056
INFO:tenpy.algorithms.purification:--> beta=0.750000, E_bond=-1.3941816805, max(S)=0.3893269224
INFO:tenpy.algorithms.purification:--> beta=0.800000, E_bond=-1.4027375341, max(S)=0.3983551258
INFO:tenpy.algorithms.purification:--> beta=0.850000, E_bond=-1.4097639704, max(S)=0.4064789716
INFO:tenpy.algorithms.purification:--> beta=0.900000, E_bond=-1.4155987118, max(S)=0.4138345769
INFO:tenpy.algorithms.purification:--> beta=0.950000, E_bond=-1.4204948990, max(S)=0.4205309967
INFO:tenpy.algorithms.purification:--> beta=1.000000, E_bond=-1.4246438886, max(S)=0.4266562441
INFO:tenpy.algorithms.purification:--> beta=1.050000, E_bond=-1.4281916564, max(S)=0.4322819527
INFO:tenpy.algorithms.purification:--> beta=1.100000, E_bond=-1.4312506251, max(S)=0.4374669632
INFO:tenpy.algorithms.purification:--> beta=1.150000, E_bond=-1.4339082222, max(S)=0.4422600755
INFO:tenpy.algorithms.purification:--> beta=1.200000, E_bond=-1.4362331058, max(S)=0.4467021603
INFO:tenpy.algorithms.purification:--> beta=1.250000, E_bond=-1.4382797183, max(S)=0.4508277821
INFO:tenpy.algorithms.purification:--> beta=1.300000, E_bond=-1.4400916410, max(S)=0.4546664509
INFO:tenpy.algorithms.purification:--> beta=1.350000, E_bond=-1.4417040823, max(S)=0.4582435927
INFO:tenpy.algorithms.purification:--> beta=1.400000, E_bond=-1.4431457386, max(S)=0.4615813050
INFO:tenpy.algorithms.purification:--> beta=1.450000, E_bond=-1.4444401956, max(S)=0.4646989497
INFO:tenpy.algorithms.purification:--> beta=1.500000, E_bond=-1.4456069943, max(S)=0.4676136203

[4, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 4]

INFO:tenpy.tools.params:TFIChain: reading 'L'=30
INFO:tenpy.tools.params:TFIChain: reading 'J'=1.0
INFO:tenpy.tools.params:TFIChain: reading 'g'=1.2
INFO:tenpy.tools.params:PurificationTEBD: subconfig 'trunc_params'=Config(<2 options>, 'trunc_params')
INFO:tenpy.tools.params:PurificationTEBD: reading 'dt'=0.05
INFO:tenpy.algorithms.tebd:Calculate U for {'order': 2, 'delta_t': 0.05, 'type_evo': 'imag', 'E_offset': None, 'tau': -0.05j}
INFO:tenpy.tools.params:trunc_params: reading 'chi_max'=20
INFO:tenpy.tools.params:trunc_params: reading 'svd_min'=1e-08
INFO:tenpy.algorithms.purification:--> beta=0.050000, E_bond=-0.2460708907, max(S)=0.0172500676
INFO:tenpy.algorithms.purification:--> beta=0.100000, E_bond=-0.4756494810, max(S)=0.0532230133
INFO:tenpy.algorithms.purification:--> beta=0.150000, E_bond=-0.6767971387, max(S)=0.0967049734
INFO:tenpy.algorithms.purification:--> beta=0.200000, E_bond=-0.8441540463, max(S)=0.1411322525
INFO:tenpy.algorithms.purification:--> beta=0.250000, E_bond=-0.9781014310, max(S)=0.1827168026
INFO:tenpy.algorithms.purification:--> beta=0.300000, E_bond=-1.0825193832, max(S)=0.2197692357
INFO:tenpy.algorithms.purification:--> beta=0.350000, E_bond=-1.1626430338, max(S)=0.2518978714
INFO:tenpy.algorithms.purification:--> beta=0.400000, E_bond=-1.2236704021, max(S)=0.2793931954
INFO:tenpy.algorithms.purification:--> beta=0.450000, E_bond=-1.2701012984, max(S)=0.3028286284
INFO:tenpy.algorithms.purification:--> beta=0.500000, E_bond=-1.3055507972, max(S)=0.3228394786
INFO:tenpy.algorithms.purification:--> beta=0.550000, E_bond=-1.3328003341, max(S)=0.3400180953
INFO:tenpy.algorithms.purification:--> beta=0.600000, E_bond=-1.3539370350, max(S)=0.3548744861
INFO:tenpy.algorithms.purification:--> beta=0.650000, E_bond=-1.3705056888, max(S)=0.3678296985
INFO:tenpy.algorithms.purification:--> beta=0.700000, E_bond=-1.3836424298, max(S)=0.3792235056
INFO:tenpy.algorithms.purification:--> beta=0.750000, E_bond=-1.3941816805, max(S)=0.3893269224
INFO:tenpy.algorithms.purification:--> beta=0.800000, E_bond=-1.4027375341, max(S)=0.3983551258
INFO:tenpy.algorithms.purification:--> beta=0.850000, E_bond=-1.4097639705, max(S)=0.4064789719
INFO:tenpy.algorithms.purification:--> beta=0.900000, E_bond=-1.4155987119, max(S)=0.4138345776
INFO:tenpy.algorithms.purification:--> beta=0.950000, E_bond=-1.4204948992, max(S)=0.4205309982
INFO:tenpy.algorithms.purification:--> beta=1.000000, E_bond=-1.4246438890, max(S)=0.4266562471
INFO:tenpy.algorithms.purification:--> beta=1.050000, E_bond=-1.4281916571, max(S)=0.4322819578
INFO:tenpy.algorithms.purification:--> beta=1.100000, E_bond=-1.4312506259, max(S)=0.4374669712
INFO:tenpy.algorithms.purification:--> beta=1.150000, E_bond=-1.4339082234, max(S)=0.4422600875
INFO:tenpy.algorithms.purification:--> beta=1.200000, E_bond=-1.4362331073, max(S)=0.4467021777
INFO:tenpy.algorithms.purification:--> beta=1.250000, E_bond=-1.4382797203, max(S)=0.4508278065
INFO:tenpy.algorithms.purification:--> beta=1.300000, E_bond=-1.4400916435, max(S)=0.4546664842
INFO:tenpy.algorithms.purification:--> beta=1.350000, E_bond=-1.4417040854, max(S)=0.4582436371
INFO:tenpy.algorithms.purification:--> beta=1.400000, E_bond=-1.4431457423, max(S)=0.4615813631
INFO:tenpy.algorithms.purification:--> beta=1.450000, E_bond=-1.4444402001, max(S)=0.4646990244
INFO:tenpy.algorithms.purification:--> beta=1.500000, E_bond=-1.4456069997, max(S)=0.4676137150

[4, 16, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 16, 4]

INFO:tenpy.tools.params:TFIChain: reading 'L'=30
INFO:tenpy.tools.params:TFIChain: reading 'J'=1.0
INFO:tenpy.tools.params:TFIChain: reading 'g'=1.2
INFO:tenpy.tools.params:PurificationTEBD: subconfig 'trunc_params'=Config(<2 options>, 'trunc_params')
INFO:tenpy.tools.params:PurificationTEBD: reading 'dt'=0.05
INFO:tenpy.algorithms.tebd:Calculate U for {'order': 2, 'delta_t': 0.05, 'type_evo': 'imag', 'E_offset': None, 'tau': -0.05j}
INFO:tenpy.tools.params:trunc_params: reading 'chi_max'=24
INFO:tenpy.tools.params:trunc_params: reading 'svd_min'=1e-08
INFO:tenpy.algorithms.purification:--> beta=0.050000, E_bond=-0.2460708907, max(S)=0.0172500676
INFO:tenpy.algorithms.purification:--> beta=0.100000, E_bond=-0.4756494810, max(S)=0.0532230133
INFO:tenpy.algorithms.purification:--> beta=0.150000, E_bond=-0.6767971387, max(S)=0.0967049734
INFO:tenpy.algorithms.purification:--> beta=0.200000, E_bond=-0.8441540463, max(S)=0.1411322525
INFO:tenpy.algorithms.purification:--> beta=0.250000, E_bond=-0.9781014310, max(S)=0.1827168026
INFO:tenpy.algorithms.purification:--> beta=0.300000, E_bond=-1.0825193832, max(S)=0.2197692357
INFO:tenpy.algorithms.purification:--> beta=0.350000, E_bond=-1.1626430338, max(S)=0.2518978714
INFO:tenpy.algorithms.purification:--> beta=0.400000, E_bond=-1.2236704021, max(S)=0.2793931954
INFO:tenpy.algorithms.purification:--> beta=0.450000, E_bond=-1.2701012984, max(S)=0.3028286284
INFO:tenpy.algorithms.purification:--> beta=0.500000, E_bond=-1.3055507972, max(S)=0.3228394786
INFO:tenpy.algorithms.purification:--> beta=0.550000, E_bond=-1.3328003341, max(S)=0.3400180953
INFO:tenpy.algorithms.purification:--> beta=0.600000, E_bond=-1.3539370350, max(S)=0.3548744861
INFO:tenpy.algorithms.purification:--> beta=0.650000, E_bond=-1.3705056888, max(S)=0.3678296985
INFO:tenpy.algorithms.purification:--> beta=0.700000, E_bond=-1.3836424298, max(S)=0.3792235056
INFO:tenpy.algorithms.purification:--> beta=0.750000, E_bond=-1.3941816805, max(S)=0.3893269224
INFO:tenpy.algorithms.purification:--> beta=0.800000, E_bond=-1.4027375341, max(S)=0.3983551258
INFO:tenpy.algorithms.purification:--> beta=0.850000, E_bond=-1.4097639705, max(S)=0.4064789719
INFO:tenpy.algorithms.purification:--> beta=0.900000, E_bond=-1.4155987119, max(S)=0.4138345776
INFO:tenpy.algorithms.purification:--> beta=0.950000, E_bond=-1.4204948992, max(S)=0.4205309982
INFO:tenpy.algorithms.purification:--> beta=1.000000, E_bond=-1.4246438890, max(S)=0.4266562471
INFO:tenpy.algorithms.purification:--> beta=1.050000, E_bond=-1.4281916571, max(S)=0.4322819578
INFO:tenpy.algorithms.purification:--> beta=1.100000, E_bond=-1.4312506260, max(S)=0.4374669712
INFO:tenpy.algorithms.purification:--> beta=1.150000, E_bond=-1.4339082234, max(S)=0.4422600875
INFO:tenpy.algorithms.purification:--> beta=1.200000, E_bond=-1.4362331074, max(S)=0.4467021777
INFO:tenpy.algorithms.purification:--> beta=1.250000, E_bond=-1.4382797204, max(S)=0.4508278067
INFO:tenpy.algorithms.purification:--> beta=1.300000, E_bond=-1.4400916437, max(S)=0.4546664848
INFO:tenpy.algorithms.purification:--> beta=1.350000, E_bond=-1.4417040858, max(S)=0.4582436383
INFO:tenpy.algorithms.purification:--> beta=1.400000, E_bond=-1.4431457429, max(S)=0.4615813653
INFO:tenpy.algorithms.purification:--> beta=1.450000, E_bond=-1.4444402010, max(S)=0.4646990279
INFO:tenpy.algorithms.purification:--> beta=1.500000, E_bond=-1.4456070009, max(S)=0.4676137204

[4, 16, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 16, 4]

datas_tebd.keys()

dict_keys([2, 4, 8, 12, 16, 20, 24])

chis = list(datas_tebd.keys())
plt.plot(chis, [datas_tebd[c]['time_sq'] for c in chis], '.', label='TEBD; sampling q')
plt.plot(chis, [datas_tebd[c]['time_nsq'] for c in chis], '.', label='TEBD; tracing q')

plt.legend()
plt.xlabel(r'$\chi$')
plt.ylabel(r'Sampling Time')
plt.show()

At these small bond dimensions, \(\chi \leq 24\), we do not see the expect scaling of sampling time with bond dimension. The transverse field Ising model is not complicated enough to generate large bond dimensions.

Accuracy with increasing number of samples

Finally, we demonstrate that the error in expectation values from sampling decreases with the number of samples, as expected.

data_dict = {}
for ns in [10, 25, 50, 100, 250, 500]:
    data_tebd = imag_tebd(L=30, beta_max=3.0, num_samples=ns)
    data_dict[ns] = data_tebd

INFO:tenpy.tools.params:TFIChain: reading 'L'=30
INFO:tenpy.tools.params:TFIChain: reading 'J'=1.0
INFO:tenpy.tools.params:TFIChain: reading 'g'=1.2
INFO:tenpy.tools.params:PurificationTEBD: subconfig 'trunc_params'=Config(<2 options>, 'trunc_params')
INFO:tenpy.tools.params:PurificationTEBD: reading 'dt'=0.05
INFO:tenpy.algorithms.tebd:Calculate U for {'order': 2, 'delta_t': 0.05, 'type_evo': 'imag', 'E_offset': None, 'tau': -0.05j}
INFO:tenpy.tools.params:trunc_params: reading 'chi_max'=100
INFO:tenpy.tools.params:trunc_params: reading 'svd_min'=1e-08
INFO:tenpy.algorithms.purification:--> beta=0.050000, E_bond=-0.2460708907, max(S)=0.0172500676

[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]

INFO:tenpy.algorithms.purification:--> beta=0.100000, E_bond=-0.4756494810, max(S)=0.0532230133

[4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4]

INFO:tenpy.algorithms.purification:--> beta=0.150000, E_bond=-0.6767971387, max(S)=0.0967049734

[4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4]

INFO:tenpy.algorithms.purification:--> beta=0.200000, E_bond=-0.8441540463, max(S)=0.1411322525

[4, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4]

INFO:tenpy.algorithms.purification:--> beta=0.250000, E_bond=-0.9781014310, max(S)=0.1827168026

[4, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 4]

INFO:tenpy.algorithms.purification:--> beta=0.300000, E_bond=-1.0825193832, max(S)=0.2197692357

[4, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 4]

INFO:tenpy.algorithms.purification:--> beta=0.350000, E_bond=-1.1626430338, max(S)=0.2518978714

[4, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 4]

INFO:tenpy.algorithms.purification:--> beta=0.400000, E_bond=-1.2236704021, max(S)=0.2793931954

[4, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 4]

INFO:tenpy.algorithms.purification:--> beta=0.450000, E_bond=-1.2701012984, max(S)=0.3028286284

[4, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 4]

INFO:tenpy.algorithms.purification:--> beta=0.500000, E_bond=-1.3055507972, max(S)=0.3228394786

[4, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 4]

INFO:tenpy.algorithms.purification:--> beta=0.550000, E_bond=-1.3328003341, max(S)=0.3400180953

[4, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 12, 4]

INFO:tenpy.algorithms.purification:--> beta=0.600000, E_bond=-1.3539370350, max(S)=0.3548744861

[4, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 12, 4]

INFO:tenpy.algorithms.purification:--> beta=0.650000, E_bond=-1.3705056888, max(S)=0.3678296985

[4, 12, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 12, 4]

INFO:tenpy.algorithms.purification:--> beta=0.700000, E_bond=-1.3836424298, max(S)=0.3792235056

[4, 13, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 13, 4]

INFO:tenpy.algorithms.purification:--> beta=0.750000, E_bond=-1.3941816805, max(S)=0.3893269224

[4, 13, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 13, 4]

INFO:tenpy.algorithms.purification:--> beta=0.800000, E_bond=-1.4027375341, max(S)=0.3983551258

[4, 14, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 16, 16, 14, 4]

INFO:tenpy.algorithms.purification:--> beta=0.850000, E_bond=-1.4097639705, max(S)=0.4064789719

[4, 14, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 14, 4]

INFO:tenpy.algorithms.purification:--> beta=0.900000, E_bond=-1.4155987119, max(S)=0.4138345776

[4, 14, 17, 17, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 17, 17, 14, 4]

INFO:tenpy.algorithms.purification:--> beta=0.950000, E_bond=-1.4204948992, max(S)=0.4205309982

[4, 15, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 15, 4]

INFO:tenpy.algorithms.purification:--> beta=1.000000, E_bond=-1.4246438890, max(S)=0.4266562471

[4, 15, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 15, 4]

INFO:tenpy.algorithms.purification:--> beta=1.050000, E_bond=-1.4281916571, max(S)=0.4322819578

[4, 16, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 15, 4]

INFO:tenpy.algorithms.purification:--> beta=1.100000, E_bond=-1.4312506260, max(S)=0.4374669712

[4, 16, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.150000, E_bond=-1.4339082234, max(S)=0.4422600875

[4, 16, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.200000, E_bond=-1.4362331074, max(S)=0.4467021777

[4, 16, 22, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 22, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.250000, E_bond=-1.4382797204, max(S)=0.4508278067

[4, 16, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.300000, E_bond=-1.4400916437, max(S)=0.4546664848

[4, 16, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.350000, E_bond=-1.4417040858, max(S)=0.4582436383

[4, 16, 23, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 23, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.400000, E_bond=-1.4431457429, max(S)=0.4615813653

[4, 16, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.450000, E_bond=-1.4444402010, max(S)=0.4646990279

[4, 16, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.500000, E_bond=-1.4456070009, max(S)=0.4676137204

[4, 16, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 16, 4]

INFO:tenpy.tools.params:TFIChain: reading 'L'=30
INFO:tenpy.tools.params:TFIChain: reading 'J'=1.0
INFO:tenpy.tools.params:TFIChain: reading 'g'=1.2
/Users/jakobunfried/tenpy/development/tenpy/tools/params.py:232: UserWarning: unused options for config PurificationTEBD:
['N_steps', 'order']
  warnings.warn(msg.format(keys=sorted(unused), name=self.name))
INFO:tenpy.tools.params:PurificationTEBD: subconfig 'trunc_params'=Config(<2 options>, 'trunc_params')
INFO:tenpy.tools.params:PurificationTEBD: reading 'dt'=0.05
INFO:tenpy.algorithms.tebd:Calculate U for {'order': 2, 'delta_t': 0.05, 'type_evo': 'imag', 'E_offset': None, 'tau': -0.05j}
INFO:tenpy.tools.params:trunc_params: reading 'chi_max'=100
INFO:tenpy.tools.params:trunc_params: reading 'svd_min'=1e-08
INFO:tenpy.algorithms.purification:--> beta=0.050000, E_bond=-0.2460708907, max(S)=0.0172500676

[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]

INFO:tenpy.algorithms.purification:--> beta=0.100000, E_bond=-0.4756494810, max(S)=0.0532230133

[4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4]

INFO:tenpy.algorithms.purification:--> beta=0.150000, E_bond=-0.6767971387, max(S)=0.0967049734

[4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4]

INFO:tenpy.algorithms.purification:--> beta=0.200000, E_bond=-0.8441540463, max(S)=0.1411322525

[4, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4]

INFO:tenpy.algorithms.purification:--> beta=0.250000, E_bond=-0.9781014310, max(S)=0.1827168026

[4, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 4]

INFO:tenpy.algorithms.purification:--> beta=0.300000, E_bond=-1.0825193832, max(S)=0.2197692357

[4, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 4]

INFO:tenpy.algorithms.purification:--> beta=0.350000, E_bond=-1.1626430338, max(S)=0.2518978714

[4, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 4]

INFO:tenpy.algorithms.purification:--> beta=0.400000, E_bond=-1.2236704021, max(S)=0.2793931954

[4, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 4]

INFO:tenpy.algorithms.purification:--> beta=0.450000, E_bond=-1.2701012984, max(S)=0.3028286284

[4, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 4]

INFO:tenpy.algorithms.purification:--> beta=0.500000, E_bond=-1.3055507972, max(S)=0.3228394786

[4, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 4]

INFO:tenpy.algorithms.purification:--> beta=0.550000, E_bond=-1.3328003341, max(S)=0.3400180953

[4, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 12, 4]

INFO:tenpy.algorithms.purification:--> beta=0.600000, E_bond=-1.3539370350, max(S)=0.3548744861

[4, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 12, 4]

INFO:tenpy.algorithms.purification:--> beta=0.650000, E_bond=-1.3705056888, max(S)=0.3678296985

[4, 12, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 12, 4]

INFO:tenpy.algorithms.purification:--> beta=0.700000, E_bond=-1.3836424298, max(S)=0.3792235056

[4, 13, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 13, 4]

INFO:tenpy.algorithms.purification:--> beta=0.750000, E_bond=-1.3941816805, max(S)=0.3893269224

[4, 13, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 13, 4]

INFO:tenpy.algorithms.purification:--> beta=0.800000, E_bond=-1.4027375341, max(S)=0.3983551258

[4, 14, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 16, 16, 14, 4]

INFO:tenpy.algorithms.purification:--> beta=0.850000, E_bond=-1.4097639705, max(S)=0.4064789719

[4, 14, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 14, 4]

INFO:tenpy.algorithms.purification:--> beta=0.900000, E_bond=-1.4155987119, max(S)=0.4138345776

[4, 14, 17, 17, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 17, 17, 14, 4]

INFO:tenpy.algorithms.purification:--> beta=0.950000, E_bond=-1.4204948992, max(S)=0.4205309982

[4, 15, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 15, 4]

INFO:tenpy.algorithms.purification:--> beta=1.000000, E_bond=-1.4246438890, max(S)=0.4266562471

[4, 15, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 15, 4]

INFO:tenpy.algorithms.purification:--> beta=1.050000, E_bond=-1.4281916571, max(S)=0.4322819578

[4, 16, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 15, 4]

INFO:tenpy.algorithms.purification:--> beta=1.100000, E_bond=-1.4312506260, max(S)=0.4374669712

[4, 16, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.150000, E_bond=-1.4339082234, max(S)=0.4422600875

[4, 16, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.200000, E_bond=-1.4362331074, max(S)=0.4467021777

[4, 16, 22, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 22, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.250000, E_bond=-1.4382797204, max(S)=0.4508278067

[4, 16, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.300000, E_bond=-1.4400916437, max(S)=0.4546664848

[4, 16, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.350000, E_bond=-1.4417040858, max(S)=0.4582436383

[4, 16, 23, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 23, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.400000, E_bond=-1.4431457429, max(S)=0.4615813653

[4, 16, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.450000, E_bond=-1.4444402010, max(S)=0.4646990279

[4, 16, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.500000, E_bond=-1.4456070009, max(S)=0.4676137204

[4, 16, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 16, 4]

INFO:tenpy.tools.params:TFIChain: reading 'L'=30
INFO:tenpy.tools.params:TFIChain: reading 'J'=1.0
INFO:tenpy.tools.params:TFIChain: reading 'g'=1.2
INFO:tenpy.tools.params:PurificationTEBD: subconfig 'trunc_params'=Config(<2 options>, 'trunc_params')
INFO:tenpy.tools.params:PurificationTEBD: reading 'dt'=0.05
INFO:tenpy.algorithms.tebd:Calculate U for {'order': 2, 'delta_t': 0.05, 'type_evo': 'imag', 'E_offset': None, 'tau': -0.05j}
INFO:tenpy.tools.params:trunc_params: reading 'chi_max'=100
INFO:tenpy.tools.params:trunc_params: reading 'svd_min'=1e-08
INFO:tenpy.algorithms.purification:--> beta=0.050000, E_bond=-0.2460708907, max(S)=0.0172500676

[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]

INFO:tenpy.algorithms.purification:--> beta=0.100000, E_bond=-0.4756494810, max(S)=0.0532230133

[4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4]

INFO:tenpy.algorithms.purification:--> beta=0.150000, E_bond=-0.6767971387, max(S)=0.0967049734

[4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4]

INFO:tenpy.algorithms.purification:--> beta=0.200000, E_bond=-0.8441540463, max(S)=0.1411322525

[4, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4]

INFO:tenpy.algorithms.purification:--> beta=0.250000, E_bond=-0.9781014310, max(S)=0.1827168026

[4, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 4]

INFO:tenpy.algorithms.purification:--> beta=0.300000, E_bond=-1.0825193832, max(S)=0.2197692357

[4, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 4]

INFO:tenpy.algorithms.purification:--> beta=0.350000, E_bond=-1.1626430338, max(S)=0.2518978714

[4, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 4]

INFO:tenpy.algorithms.purification:--> beta=0.400000, E_bond=-1.2236704021, max(S)=0.2793931954

[4, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 4]

INFO:tenpy.algorithms.purification:--> beta=0.450000, E_bond=-1.2701012984, max(S)=0.3028286284

[4, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 4]

INFO:tenpy.algorithms.purification:--> beta=0.500000, E_bond=-1.3055507972, max(S)=0.3228394786

[4, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 4]

INFO:tenpy.algorithms.purification:--> beta=0.550000, E_bond=-1.3328003341, max(S)=0.3400180953

[4, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 12, 4]

INFO:tenpy.algorithms.purification:--> beta=0.600000, E_bond=-1.3539370350, max(S)=0.3548744861

[4, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 12, 4]

INFO:tenpy.algorithms.purification:--> beta=0.650000, E_bond=-1.3705056888, max(S)=0.3678296985

[4, 12, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 12, 4]

INFO:tenpy.algorithms.purification:--> beta=0.700000, E_bond=-1.3836424298, max(S)=0.3792235056

[4, 13, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 13, 4]

INFO:tenpy.algorithms.purification:--> beta=0.750000, E_bond=-1.3941816805, max(S)=0.3893269224

[4, 13, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 13, 4]

INFO:tenpy.algorithms.purification:--> beta=0.800000, E_bond=-1.4027375341, max(S)=0.3983551258

[4, 14, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 16, 16, 14, 4]

INFO:tenpy.algorithms.purification:--> beta=0.850000, E_bond=-1.4097639705, max(S)=0.4064789719

[4, 14, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 14, 4]

INFO:tenpy.algorithms.purification:--> beta=0.900000, E_bond=-1.4155987119, max(S)=0.4138345776

[4, 14, 17, 17, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 17, 17, 14, 4]

INFO:tenpy.algorithms.purification:--> beta=0.950000, E_bond=-1.4204948992, max(S)=0.4205309982

[4, 15, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 15, 4]

INFO:tenpy.algorithms.purification:--> beta=1.000000, E_bond=-1.4246438890, max(S)=0.4266562471

[4, 15, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 15, 4]

INFO:tenpy.algorithms.purification:--> beta=1.050000, E_bond=-1.4281916571, max(S)=0.4322819578

[4, 16, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 15, 4]

INFO:tenpy.algorithms.purification:--> beta=1.100000, E_bond=-1.4312506260, max(S)=0.4374669712

[4, 16, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.150000, E_bond=-1.4339082234, max(S)=0.4422600875

[4, 16, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.200000, E_bond=-1.4362331074, max(S)=0.4467021777

[4, 16, 22, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 22, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.250000, E_bond=-1.4382797204, max(S)=0.4508278067

[4, 16, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.300000, E_bond=-1.4400916437, max(S)=0.4546664848

[4, 16, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.350000, E_bond=-1.4417040858, max(S)=0.4582436383

[4, 16, 23, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 23, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.400000, E_bond=-1.4431457429, max(S)=0.4615813653

[4, 16, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.450000, E_bond=-1.4444402010, max(S)=0.4646990279

[4, 16, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.500000, E_bond=-1.4456070009, max(S)=0.4676137204

[4, 16, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 16, 4]

INFO:tenpy.tools.params:TFIChain: reading 'L'=30
INFO:tenpy.tools.params:TFIChain: reading 'J'=1.0
INFO:tenpy.tools.params:TFIChain: reading 'g'=1.2
INFO:tenpy.tools.params:PurificationTEBD: subconfig 'trunc_params'=Config(<2 options>, 'trunc_params')
INFO:tenpy.tools.params:PurificationTEBD: reading 'dt'=0.05
INFO:tenpy.algorithms.tebd:Calculate U for {'order': 2, 'delta_t': 0.05, 'type_evo': 'imag', 'E_offset': None, 'tau': -0.05j}
INFO:tenpy.tools.params:trunc_params: reading 'chi_max'=100
INFO:tenpy.tools.params:trunc_params: reading 'svd_min'=1e-08
INFO:tenpy.algorithms.purification:--> beta=0.050000, E_bond=-0.2460708907, max(S)=0.0172500676

[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]

INFO:tenpy.algorithms.purification:--> beta=0.100000, E_bond=-0.4756494810, max(S)=0.0532230133

[4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4]

INFO:tenpy.algorithms.purification:--> beta=0.150000, E_bond=-0.6767971387, max(S)=0.0967049734

[4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4]

INFO:tenpy.algorithms.purification:--> beta=0.200000, E_bond=-0.8441540463, max(S)=0.1411322525

[4, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4]

INFO:tenpy.algorithms.purification:--> beta=0.250000, E_bond=-0.9781014310, max(S)=0.1827168026

[4, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 4]

INFO:tenpy.algorithms.purification:--> beta=0.300000, E_bond=-1.0825193832, max(S)=0.2197692357

[4, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 4]

INFO:tenpy.algorithms.purification:--> beta=0.350000, E_bond=-1.1626430338, max(S)=0.2518978714

[4, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 4]

INFO:tenpy.algorithms.purification:--> beta=0.400000, E_bond=-1.2236704021, max(S)=0.2793931954

[4, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 4]

INFO:tenpy.algorithms.purification:--> beta=0.450000, E_bond=-1.2701012984, max(S)=0.3028286284

[4, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 4]

INFO:tenpy.algorithms.purification:--> beta=0.500000, E_bond=-1.3055507972, max(S)=0.3228394786

[4, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 4]

INFO:tenpy.algorithms.purification:--> beta=0.550000, E_bond=-1.3328003341, max(S)=0.3400180953

[4, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 12, 4]

INFO:tenpy.algorithms.purification:--> beta=0.600000, E_bond=-1.3539370350, max(S)=0.3548744861

[4, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 12, 4]

INFO:tenpy.algorithms.purification:--> beta=0.650000, E_bond=-1.3705056888, max(S)=0.3678296985

[4, 12, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 12, 4]

INFO:tenpy.algorithms.purification:--> beta=0.700000, E_bond=-1.3836424298, max(S)=0.3792235056

[4, 13, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 13, 4]

INFO:tenpy.algorithms.purification:--> beta=0.750000, E_bond=-1.3941816805, max(S)=0.3893269224

[4, 13, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 13, 4]

INFO:tenpy.algorithms.purification:--> beta=0.800000, E_bond=-1.4027375341, max(S)=0.3983551258

[4, 14, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 16, 16, 14, 4]

INFO:tenpy.algorithms.purification:--> beta=0.850000, E_bond=-1.4097639705, max(S)=0.4064789719

[4, 14, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 14, 4]

INFO:tenpy.algorithms.purification:--> beta=0.900000, E_bond=-1.4155987119, max(S)=0.4138345776

[4, 14, 17, 17, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 17, 17, 14, 4]

INFO:tenpy.algorithms.purification:--> beta=0.950000, E_bond=-1.4204948992, max(S)=0.4205309982

[4, 15, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 15, 4]

INFO:tenpy.algorithms.purification:--> beta=1.000000, E_bond=-1.4246438890, max(S)=0.4266562471

[4, 15, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 15, 4]

INFO:tenpy.algorithms.purification:--> beta=1.050000, E_bond=-1.4281916571, max(S)=0.4322819578

[4, 16, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 15, 4]

INFO:tenpy.algorithms.purification:--> beta=1.100000, E_bond=-1.4312506260, max(S)=0.4374669712

[4, 16, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.150000, E_bond=-1.4339082234, max(S)=0.4422600875

[4, 16, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.200000, E_bond=-1.4362331074, max(S)=0.4467021777

[4, 16, 22, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 22, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.250000, E_bond=-1.4382797204, max(S)=0.4508278067

[4, 16, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.300000, E_bond=-1.4400916437, max(S)=0.4546664848

[4, 16, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.350000, E_bond=-1.4417040858, max(S)=0.4582436383

[4, 16, 23, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 23, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.400000, E_bond=-1.4431457429, max(S)=0.4615813653

[4, 16, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.450000, E_bond=-1.4444402010, max(S)=0.4646990279

[4, 16, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.500000, E_bond=-1.4456070009, max(S)=0.4676137204

[4, 16, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 16, 4]

INFO:tenpy.tools.params:TFIChain: reading 'L'=30
INFO:tenpy.tools.params:TFIChain: reading 'J'=1.0
INFO:tenpy.tools.params:TFIChain: reading 'g'=1.2
INFO:tenpy.tools.params:PurificationTEBD: subconfig 'trunc_params'=Config(<2 options>, 'trunc_params')
INFO:tenpy.tools.params:PurificationTEBD: reading 'dt'=0.05
INFO:tenpy.algorithms.tebd:Calculate U for {'order': 2, 'delta_t': 0.05, 'type_evo': 'imag', 'E_offset': None, 'tau': -0.05j}
INFO:tenpy.tools.params:trunc_params: reading 'chi_max'=100
INFO:tenpy.tools.params:trunc_params: reading 'svd_min'=1e-08
INFO:tenpy.algorithms.purification:--> beta=0.050000, E_bond=-0.2460708907, max(S)=0.0172500676

[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]

INFO:tenpy.algorithms.purification:--> beta=0.100000, E_bond=-0.4756494810, max(S)=0.0532230133

[4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4]

INFO:tenpy.algorithms.purification:--> beta=0.150000, E_bond=-0.6767971387, max(S)=0.0967049734

[4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4]

INFO:tenpy.algorithms.purification:--> beta=0.200000, E_bond=-0.8441540463, max(S)=0.1411322525

[4, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4]

INFO:tenpy.algorithms.purification:--> beta=0.250000, E_bond=-0.9781014310, max(S)=0.1827168026

[4, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 4]

INFO:tenpy.algorithms.purification:--> beta=0.300000, E_bond=-1.0825193832, max(S)=0.2197692357

[4, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 4]

INFO:tenpy.algorithms.purification:--> beta=0.350000, E_bond=-1.1626430338, max(S)=0.2518978714

[4, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 4]

INFO:tenpy.algorithms.purification:--> beta=0.400000, E_bond=-1.2236704021, max(S)=0.2793931954

[4, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 4]

INFO:tenpy.algorithms.purification:--> beta=0.450000, E_bond=-1.2701012984, max(S)=0.3028286284

[4, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 4]

INFO:tenpy.algorithms.purification:--> beta=0.500000, E_bond=-1.3055507972, max(S)=0.3228394786

[4, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 4]

INFO:tenpy.algorithms.purification:--> beta=0.550000, E_bond=-1.3328003341, max(S)=0.3400180953

[4, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 12, 4]

INFO:tenpy.algorithms.purification:--> beta=0.600000, E_bond=-1.3539370350, max(S)=0.3548744861

[4, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 12, 4]

INFO:tenpy.algorithms.purification:--> beta=0.650000, E_bond=-1.3705056888, max(S)=0.3678296985

[4, 12, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 12, 4]

INFO:tenpy.algorithms.purification:--> beta=0.700000, E_bond=-1.3836424298, max(S)=0.3792235056

[4, 13, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 13, 4]

INFO:tenpy.algorithms.purification:--> beta=0.750000, E_bond=-1.3941816805, max(S)=0.3893269224

[4, 13, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 13, 4]

INFO:tenpy.algorithms.purification:--> beta=0.800000, E_bond=-1.4027375341, max(S)=0.3983551258

[4, 14, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 16, 16, 14, 4]

INFO:tenpy.algorithms.purification:--> beta=0.850000, E_bond=-1.4097639705, max(S)=0.4064789719

[4, 14, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 14, 4]

INFO:tenpy.algorithms.purification:--> beta=0.900000, E_bond=-1.4155987119, max(S)=0.4138345776

[4, 14, 17, 17, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 17, 17, 14, 4]

INFO:tenpy.algorithms.purification:--> beta=0.950000, E_bond=-1.4204948992, max(S)=0.4205309982

[4, 15, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 15, 4]

INFO:tenpy.algorithms.purification:--> beta=1.000000, E_bond=-1.4246438890, max(S)=0.4266562471

[4, 15, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 15, 4]

INFO:tenpy.algorithms.purification:--> beta=1.050000, E_bond=-1.4281916571, max(S)=0.4322819578

[4, 16, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 15, 4]

INFO:tenpy.algorithms.purification:--> beta=1.100000, E_bond=-1.4312506260, max(S)=0.4374669712

[4, 16, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.150000, E_bond=-1.4339082234, max(S)=0.4422600875

[4, 16, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.200000, E_bond=-1.4362331074, max(S)=0.4467021777

[4, 16, 22, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 22, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.250000, E_bond=-1.4382797204, max(S)=0.4508278067

[4, 16, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.300000, E_bond=-1.4400916437, max(S)=0.4546664848

[4, 16, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.350000, E_bond=-1.4417040858, max(S)=0.4582436383

[4, 16, 23, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 23, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.400000, E_bond=-1.4431457429, max(S)=0.4615813653

[4, 16, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.450000, E_bond=-1.4444402010, max(S)=0.4646990279

[4, 16, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.500000, E_bond=-1.4456070009, max(S)=0.4676137204

[4, 16, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 16, 4]

INFO:tenpy.tools.params:TFIChain: reading 'L'=30
INFO:tenpy.tools.params:TFIChain: reading 'J'=1.0
INFO:tenpy.tools.params:TFIChain: reading 'g'=1.2
INFO:tenpy.tools.params:PurificationTEBD: subconfig 'trunc_params'=Config(<2 options>, 'trunc_params')
INFO:tenpy.tools.params:PurificationTEBD: reading 'dt'=0.05
INFO:tenpy.algorithms.tebd:Calculate U for {'order': 2, 'delta_t': 0.05, 'type_evo': 'imag', 'E_offset': None, 'tau': -0.05j}
INFO:tenpy.tools.params:trunc_params: reading 'chi_max'=100
INFO:tenpy.tools.params:trunc_params: reading 'svd_min'=1e-08
INFO:tenpy.algorithms.purification:--> beta=0.050000, E_bond=-0.2460708907, max(S)=0.0172500676

[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]

INFO:tenpy.algorithms.purification:--> beta=0.100000, E_bond=-0.4756494810, max(S)=0.0532230133

[4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4]

INFO:tenpy.algorithms.purification:--> beta=0.150000, E_bond=-0.6767971387, max(S)=0.0967049734

[4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4]

INFO:tenpy.algorithms.purification:--> beta=0.200000, E_bond=-0.8441540463, max(S)=0.1411322525

[4, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4]

INFO:tenpy.algorithms.purification:--> beta=0.250000, E_bond=-0.9781014310, max(S)=0.1827168026

[4, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 4]

INFO:tenpy.algorithms.purification:--> beta=0.300000, E_bond=-1.0825193832, max(S)=0.2197692357

[4, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 4]

INFO:tenpy.algorithms.purification:--> beta=0.350000, E_bond=-1.1626430338, max(S)=0.2518978714

[4, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 4]

INFO:tenpy.algorithms.purification:--> beta=0.400000, E_bond=-1.2236704021, max(S)=0.2793931954

[4, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 4]

INFO:tenpy.algorithms.purification:--> beta=0.450000, E_bond=-1.2701012984, max(S)=0.3028286284

[4, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 4]

INFO:tenpy.algorithms.purification:--> beta=0.500000, E_bond=-1.3055507972, max(S)=0.3228394786

[4, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 4]

INFO:tenpy.algorithms.purification:--> beta=0.550000, E_bond=-1.3328003341, max(S)=0.3400180953

[4, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 12, 4]

INFO:tenpy.algorithms.purification:--> beta=0.600000, E_bond=-1.3539370350, max(S)=0.3548744861

[4, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 12, 4]

INFO:tenpy.algorithms.purification:--> beta=0.650000, E_bond=-1.3705056888, max(S)=0.3678296985

[4, 12, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 12, 4]

INFO:tenpy.algorithms.purification:--> beta=0.700000, E_bond=-1.3836424298, max(S)=0.3792235056

[4, 13, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 13, 4]

INFO:tenpy.algorithms.purification:--> beta=0.750000, E_bond=-1.3941816805, max(S)=0.3893269224

[4, 13, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 13, 4]

INFO:tenpy.algorithms.purification:--> beta=0.800000, E_bond=-1.4027375341, max(S)=0.3983551258

[4, 14, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 16, 16, 14, 4]

INFO:tenpy.algorithms.purification:--> beta=0.850000, E_bond=-1.4097639705, max(S)=0.4064789719

[4, 14, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 14, 4]

INFO:tenpy.algorithms.purification:--> beta=0.900000, E_bond=-1.4155987119, max(S)=0.4138345776

[4, 14, 17, 17, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 17, 17, 14, 4]

INFO:tenpy.algorithms.purification:--> beta=0.950000, E_bond=-1.4204948992, max(S)=0.4205309982

[4, 15, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 15, 4]

INFO:tenpy.algorithms.purification:--> beta=1.000000, E_bond=-1.4246438890, max(S)=0.4266562471

[4, 15, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 15, 4]

INFO:tenpy.algorithms.purification:--> beta=1.050000, E_bond=-1.4281916571, max(S)=0.4322819578

[4, 16, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 15, 4]

INFO:tenpy.algorithms.purification:--> beta=1.100000, E_bond=-1.4312506260, max(S)=0.4374669712

[4, 16, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.150000, E_bond=-1.4339082234, max(S)=0.4422600875

[4, 16, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.200000, E_bond=-1.4362331074, max(S)=0.4467021777

[4, 16, 22, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 22, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.250000, E_bond=-1.4382797204, max(S)=0.4508278067

[4, 16, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.300000, E_bond=-1.4400916437, max(S)=0.4546664848

[4, 16, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.350000, E_bond=-1.4417040858, max(S)=0.4582436383

[4, 16, 23, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 23, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.400000, E_bond=-1.4431457429, max(S)=0.4615813653

[4, 16, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.450000, E_bond=-1.4444402010, max(S)=0.4646990279

[4, 16, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 16, 4]

INFO:tenpy.algorithms.purification:--> beta=1.500000, E_bond=-1.4456070009, max(S)=0.4676137204

[4, 16, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 16, 4]

# note: this cell is skipped in pytest
for ns in [10, 25, 50, 100, 250, 500]:
    plt.plot(data_dict[ns]['beta'], np.sum(data_dict[ns]['Sz'], axis=1), label='TEBD')
    plt.plot(data_dict[ns]['beta'], np.sum(data_dict[ns]['Sz_sample_sq'], axis=1), '.', label='TEBD; sampling q')
    plt.plot(data_dict[ns]['beta'], np.sum(data_dict[ns]['Sz_sample_nsq'], axis=1), '.', label='TEBD; tracing q')

    plt.legend()
    plt.xlabel(r'$\beta$')
    plt.ylabel(r'total $S^z$')
    plt.title(f"Number of samples: {ns}")
    plt.show()

plt.plot([10, 25, 50, 100, 250, 500],
         [np.power(np.sum(data_dict[ns]['Sz'], axis=1) - np.sum(data_dict[ns]['Sz_sample_sq'], axis=1), 2).sum() for ns in[10, 25, 50, 100, 250, 500]],
        marker='s', label='sampling q')
plt.plot([10, 25, 50, 100, 250, 500],
         [np.power(np.sum(data_dict[ns]['Sz'], axis=1) - np.sum(data_dict[ns]['Sz_sample_nsq'], axis=1), 2).sum() for ns in[10, 25, 50, 100, 250, 500]],
        marker='s', label='tracing q')

plt.legend()
plt.xlabel(r'Num Samples')
plt.ylabel(r'$\sum_\beta \left[\sum_i (S_z^{exact}(i,\beta) - S_z^{sampling}(i,\beta))\right]^2$')
plt.show()