Auxiliary-field Monte Carlo for Quantum Spin and Boson Systems

TL;DR

This paper introduces a new auxiliary-field Monte Carlo algorithm for simulating quantum spin and boson systems, effectively handling certain models without the minus-sign problem, and demonstrates its application on various models.

Contribution

The paper presents a novel auxiliary-field Monte Carlo method based on Trotter decomposition and auxiliary Ising spins, applicable to a wide range of quantum systems.

Findings

Effective simulation of the Ising model in a transverse field without the minus-sign problem.

Successful application to the spin-1/2 XY model and disordered transverse Ising model.

Analysis of phase transitions in the two-dimensional Ising model with transverse field.

Abstract

We describe a new algorithm for the numerical simulation of quantum spin and boson systems. The method is based on the Trotter decomposition in imaginary time and a decoupling by auxiliary Ising spins. It can be applied, in principle, to arbitrary (random) spin systems, however in general it suffers from the ``minus-sign problem''. This problem is absent in the case of the Ising model in a transverse field in arbitrary dimensions and geometries. We show test results for the spin--1/2 XY model, the one--dimensional transverse Ising model with disorder, and the phase transition induced by a transverse field in the two-dimensional Ising model.