Asymptotic sign free in interacting fermion models

TL;DR

This paper introduces the concept of asymptotic sign free behavior in interacting fermion models, where the sign problem diminishes with system size and vanishes in the thermodynamic limit, enabling more effective quantum Monte Carlo simulations.

Contribution

It is the first demonstration of models exhibiting asymptotic sign free behavior, expanding the potential of QMC methods for studying correlated fermionic systems.

Findings

Sign problem diminishes with increasing system size

Sign problem disappears in the thermodynamic limit

Heuristic understanding based on renormalization-group ideas

Abstract

As an intrinsically-unbiased approach, quantum Monte Carlo (QMC) is of vital importance in understanding correlated phases of matter. Unfortunately, it often suffers notorious sign problem when simulating interacting fermion models. Here, we show for the first time that there exist interacting fermion models whose sign problem becomes less severe for larger system sizes and eventually disappears in the thermodynamic limit, which we dub as "asymptotic sign free". We demonstrate asymptotically-free sign in determinant QMC for various interacting models. Moreover, based on renormalization-group-like ideas we propose a heuristic understanding of the feature of asymptotic sign free. We believe that asymptotic sign free behavior could shed new lights to deepening our understanding of sign problem. More importantly, it can provide a promising way to decipher intriguing physics in correlated models which were conventionally thought not accessible by QMC.