A4 - Quantum ising models

In this section, we introduce ising model with quantum effects (mainly transverse magnetic fields).

First, let us define the Graph and determine \(J_{ij}, h_i\).

import cxxjij.graph as G
# set the size of problem 100
N = 100

graph = G.Dense(N)

import numpy as np
mu, sigma = 0, 1

for i in range(N):
    for j in range(N):
        # normalize with 1/N to avoid large Jij
        graph[i,j] = 0 if i == j else np.random.normal()/N

for i in range(N):
    graph[i] = np.random.normal()/N

Transeverse field ising model

In this case, transverse field ising model is used for the system.

\begin{align} H &= s \left(\sum_{i

Continuous imaginary-time quantum MonteCarlo