Elucidating the sign problem through noise distributions

TL;DR

This paper investigates the sign problem in lattice QCD at finite densities by analyzing noise distributions in two formulations of a reduced Nambu-Jona-Lasinio model, revealing conditions that mitigate the sign problem.

Contribution

It compares two formulations of a reduced NJL model, identifying one with a severe sign problem and another without, and demonstrates the use of cumulant expansion techniques to analyze noise distributions.

Findings

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

The other formulation shows no sign problem and a distribution suitable for cumulant expansion.

The study provides insights into mitigating the sign problem in lattice QCD simulations.

Abstract

Due to the presence of light pions in the theory, lattice QCD at finite densities suffers from issues with noise in both grand canonical and canonical formulations. We study two different formulations of the Nambu-Jona-Lasinio model reduced to 2+1 dimensions at large N, where N is the number of flavors. At finite chemical potential one formulation has a severe sign problem and a fermion correlator which displays a broad probability distribution with small mean. In the other we find no sign problem and a distribution amenable to the cumulant expansion techniques developed in earlier work.