Stochastic series expansion method for quantum Ising models with arbitrary interactions

TL;DR

This paper introduces a stochastic series expansion quantum Monte Carlo algorithm for the transverse Ising model with arbitrary interactions, improving computational efficiency especially for long-range interactions.

Contribution

The paper develops a novel stochastic series expansion method that reduces computational complexity for models with arbitrary interactions, including long-range cases.

Findings

Reduces scaling from N^2 to Nln(N) for long-range interactions.

Successfully tested on 1D ferromagnet with 1/r^2 decay.

Avoids interaction summations in conventional methods.

Abstract

A quantum Monte Carlo algorithm for the transverse Ising model with arbitrary short- or long-range interactions is presented. The algorithm is based on sampling the diagonal matrix elements of the power series expansion of the density matrix (stochastic series expansion), and avoids the interaction summations necessary in conventional methods. In the case of long-range interactions, the scaling of the computation time with the system size N is therefore reduced from N^2 to Nln(N). The method is tested on a one-dimensional ferromagnet in a transverse field, with interactions decaying as 1/r^2.