Reducing autocorrelation time in determinant quantum Monte Carlo using Wang-Landau algorithm: application to Holstein model

TL;DR

This paper introduces a Wang-Landau algorithm enhancement for determinant quantum Monte Carlo to significantly reduce autocorrelation times, enabling more efficient simulations of models like the Holstein model with long autocorrelation issues.

Contribution

The paper presents a novel application of the Wang-Landau algorithm to determinant quantum Monte Carlo, effectively reducing autocorrelation times in challenging lattice fermion models.

Findings

Reduced autocorrelation times in Holstein model simulations.

Effective flat-histogram sampling in configuration space.

Potential to simulate models previously limited by autocorrelation issues.

Abstract

When performing a Monte Carlo calculation, the running time should in principle be much longer than the autocorrelation time in order to get reliable results. Among different lattice fermion models, the Holstein model is notorious for its particularly long autocorrelation time. In this work, we employ the Wang-Landau algorithm in the determinant quantum Monte Carlo to achieve the flat-histogram sampling in the "configuration weight space", which can greatly reduce the autocorrelation time by sacrificing some sampling efficiency. The proposal is checked in the Holstein model on both square and honeycomb lattices. Based on such a Wang-Landau assisted determinant quantum Monte Carlo method, some models with long autocorrelation times can now be simulated possibly.