A sign-blocking method for mitigating the fermion sign problem

TL;DR

This paper introduces a sign-blocking method that improves the simulation of fermionic systems by mitigating the fermion sign problem, validated on the 2D Fermi-Hubbard model with results matching state-of-the-art benchmarks.

Contribution

The paper presents a novel sign-blocking post-processing technique that enhances the accuracy of fermionic system simulations without altering importance sampling.

Findings

Results align with existing benchmarks even in challenging regimes.

The method uncovers correlations between energy and sign factors.

It shows promise for complex quantum systems when combined with auxiliary-field formalisms.

Abstract

The fermion sign problem remains the primary obstacle in simulating the thermodynamic properties of various fermionic systems. In this work, we present a sign-blocking method to mitigate the numerical instability inherent in the sign problem. In the sign-blocking method, the Monte Carlo importance sampling remains identical to traditional methods; instead, the sign-blocking method is applied during the post-processing of signed samples. Given the significant progress in simulating the 2D Fermi-Hubbard model over the past decade, a wealth of energy benchmarks is available for comparison. Consequently, we use the 2D Fermi-Hubbard model as a benchmark to validate the sign-blocking method. Surprisingly, our results align exceptionally well with existing state-of-the-art benchmarks, even in regimes previously considered challenging. The physical mechanism of the sign-blocking method lies in uncovering the correlation between energy and sign factors through data blocking, thereby successfully inferring the fermionic system's energy. Our findings suggest that the sign-blocking method holds promise for complex quantum systems, particularly when combined with appropriate simulation techniques such as auxiliary-field formalisms that trace out the fermionic degrees of freedom.