Lee-Yang zero analysis for the study of QCD phase structure

TL;DR

This paper examines the use of Lee-Yang zero analysis to study the phase structure of QCD, highlighting how the sign problem affects the interpretation of zeros and proposing alternative insights for identifying critical points.

Contribution

It demonstrates the impact of the sign problem on Lee-Yang zero analysis in finite volume scaling and suggests focusing on zero distribution for better phase transition insights.

Findings

Sign problem causes serious issues in finite volume scaling analysis.

Lee-Yang zeros approach the real axis at large volume due to sign problem.

Distribution of zeros may be more informative than scaling behavior.

Abstract

We comment on the Lee-Yang zero analysis for the study of the phase structure of QCD at high temperature and baryon number density by Monte-Carlo simulations. We find that the sign problem for non-zero density QCD induces a serious problem in the finite volume scaling analysis of the Lee-Yang zeros for the investigation of the order of the phase transition. If the sign problem occurs at large volume, the Lee-Yang zeros will always approach the real axis of the complex parameter plane in the thermodynamic limit. This implies that a scaling behavior which would suggest a crossover transition will not be obtained. To clarify this problem, we discuss the Lee-Yang zero analysis for SU(3) pure gauge theory as a simple example without the sign problem, and then consider the case of non-zero density QCD. It is suggested that the distribution of the Lee-Yang zeros in the complex parameter space obtained by each simulation could be more important information for the investigation of the critical endpoint in the $(T, \mu_q)$ plane than the finite volume scaling behavior.