Sign problems, noise, and chiral symmetry breaking in a QCD-like theory

TL;DR

This paper compares two formulations of a 2+1D NJL model at finite chemical potential, analyzing their sign problems and fermion correlator distributions to gain insights relevant to QCD.

Contribution

It introduces and analyzes two different path integral formulations of a QCD-like model, highlighting their distinct sign problem behaviors and correlator distribution properties.

Findings

One formulation exhibits a severe sign problem with a broad correlator distribution.

The other formulation has a positive, heavy-tailed distribution suitable for cumulant expansion.

Implications for QCD are discussed based on the model's behavior.

Abstract

The Nambu-Jona-Lasinio model reduced to 2+1 dimensions has two different path integral formulations: at finite chemical potential one formulation has a severe sign problem similar to that found in QCD, while the other does not. At large N, where N is the number of flavors, one can compute the probability distributions of fermion correlators analytically in both formulations. In the former case one finds a broad distribution with small mean; in the latter one finds a heavy tailed positive distribution amenable to the cumulant expansion techniques developed in earlier work. We speculate on the implications of this model for QCD.