A Random Matrix Study of the QCD Sign Problem

TL;DR

This paper uses a random matrix model to analyze the sign problem in QCD at finite temperature and chemical potential, providing analytic expressions and identifying regions of maximal severity related to pion condensation.

Contribution

It offers an analytic expression for the average phase factor in a QCD random matrix model and maps the domain of the maximal sign problem, including its relation to the pion condensation phase.

Findings

Sign problem less severe at higher temperatures

Maximal sign problem domain linked to pion condensation

Critical point lies within the maximal sign problem region

Abstract

We investigate the severity of the sign problem in a random matrix model for QCD at finite temperature T and baryon chemical potential mu. We obtain analytic expression for the average phase factor -- the measure of the severity of the sign problem at arbitrary T and mu. We observe that the sign problem becomes less severe as the temperature is increased. We also find the domain where the sign problem is maximal -- the average phase factor is zero, which is related to the pion condensation phase in the QCD with finite isospin chemical potential. We find that, in the matrix model we studied, the critical point is located inside the domain of the maximal sign problem, making the point inaccessible to conventional reweighting techniques. We observe and describe the scaling behavior of the size and shape of the pion condensation near the chiral limit.