Reduction of the sign problem using the meron-cluster approach

TL;DR

This paper explores how the meron-cluster approach can be used to reduce the sign problem in quantum Monte Carlo simulations across a broader range of models, improving computational feasibility.

Contribution

It demonstrates that the meron-cluster method can be adapted to lessen the sign problem in models where it previously only solved it exactly, especially in intermediate parameter regimes.

Findings

Meron-cluster approach reduces the sign problem in a wider class of models.

The average sign decreases exponentially with system size, but with a different prefactor.

The sign problem is slowest to decrease near points where the meron solution fully eliminates it.

Abstract

The sign problem in quantum Monte Carlo calculations is analyzed using the meron-cluster solution. The concept of merons can be used to solve the sign problem for a limited class of models. Here we show that the method can be used to \textit{reduce} the sign problem in a wider class of models. We investigate how the meron solution evolves between a point in parameter space where it eliminates the sign problem and a point where it does not affect the sign problem at all. In this intermediate regime the merons can be used to reduce the sign problem. The average sign still decreases exponentially with system size and inverse temperature but with a different prefactor. The sign exhibits the slowest decrease in the vicinity of points where the meron-cluster solution eliminates the sign problem. We have used stochastic series expansion quantum Monte Carlo combined with the concept of directed loops.