classical_tfim_ground_state.py

import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
from xmps.iOptimize import find_ground_state
from xmps.iMPS import iMPS
from xmps.iTDVP import Trajectory
import scipy.integrate as integrate

def infinite_gs_energy(J, g):
    """For comparison: Calculate groundstate energy density of an infinite system.
    The analytic formula stems from mapping the model to free fermions, see
    P. Pfeuty, The one-dimensional Ising model with a transverse field},
    Annals of Physics 57, p. 79 (1970).
    Note that we use Pauli matrices compared this reference using spin-1/2 matrices
    and replace the sum_k -> integral dk/2pi to obtain the result in the N-> infinity limit.
    """
    def f(k, lambda_):
        return np.sqrt(1 + lambda_**2 + 2 * lambda_ * np.cos(k))

    E0_exact = - g/(J*2.*np.pi) * integrate.quad(f, -np.pi, np.pi, args=(J/g, ))[0]
    return E0_exact


if __name__ == '__main__':

    df = pd.read_csv('data/gs_data/reference_gs_energy.csv')
    gs = df['g'].to_list()

    J = -1
    Es = []
    Es_tdvp=[]
    Exact_Es = []
    for g in gs:
    
        Exact_Es.append(infinite_gs_energy(-J,g))

    np.save("tfim_exact_gs.npy", Exact_Es)

    plt.plot(gs, Exact_Es, label = "Exact")

    plt.plot(gs, df['Energy'], label = "Circuit")
    plt.legend()    
    plt.show()