Fermion bag solutions to some sign problems in four-fermion field theories

TL;DR

This paper demonstrates that reformulating certain four-fermion lattice models in the fermion bag approach eliminates sign problems, enabling rigorous solutions for models previously hindered by computational difficulties.

Contribution

The study introduces the fermion bag approach as a solution to sign problems in four-fermion models with chiral symmetries, a significant advancement over auxiliary field methods.

Findings

Sign problems are eliminated in the fermion bag formulation.

Models can be solved rigorously for the first time.

Fermion bag approach improves computational feasibility.

Abstract

Lattice four-fermion models containing $N$ flavors of staggered fermions, that are invariant under $Z_2$ and U(1) chiral symmetries, are known to suffer from sign problems when formulated using the auxiliary field approach. Although these problems have been ignored in previous studies, they can be severe. Here we show that the sign problems disappear when the models are formulated in the fermion bag approach, allowing us to solve them rigorously for the first time.