Model study of the sign problem in a mean-field approximation

TL;DR

This paper investigates the sign problem in fermion determinants at nonzero baryon chemical potential using a simplified QCD-inspired model, revealing differences between SU(2) and SU(3) color cases and applying mean-field and phase-reweighting methods.

Contribution

It demonstrates the presence or absence of the sign problem in a mean-field approximation for different gauge groups and explores estimation techniques for thermodynamic quantities.

Findings

No sign problem for SU(2) in mean-field approximation.

Sign problem persists for SU(3) even at mean-field level.

Phase-reweighting combined with mean-field provides estimates of thermodynamics.

Abstract

We study the sign problem of the fermion determinant at nonzero baryon chemical potential. For this purpose we apply a simple model derived from Quantum Chromodynamics, in the limit of large chemical potential and mass. For SU(2) color, there is no sign problem and the mean-field approximation is similar to data from the lattice. For SU(3) color the sign problem is unavoidable, even in a mean-field approximation. We apply a phase-reweighting method, combined with the mean-field approximation, to estimate thermodynamic quantities. We also investigate the mean-field free energy using a saddle-point approximation.