On the sign problem in dense QCD

TL;DR

This paper analyzes the sign problem in dense QCD, showing it is generally severe across the phase diagram and proposing a Monte Carlo method for regions with a mild sign problem.

Contribution

It provides a theoretical framework for understanding the severity of the sign problem in dense QCD and introduces a Monte Carlo technique for challenging regions.

Findings

Sign problem is severe in most of the phase diagram.

Zero chemical potential is an exception where the sign problem is mild.

A Monte Carlo method is proposed for regions with small Z-/Z+ ratio.

Abstract

We investigate the Euclidean path integral formulation of QCD at finite baryon density and temperature. We show that the partition function Z can be written as a difference between two sums Z+ and Z-, each of which defines a partition function with positive weights. We call the sign problem severe if the ratio Z-/Z+ is nonzero in the infinite volume limit. This occurs only if, and generically always if, the associated free energy densities F+ and F- are equal in this limit. We present strong evidence here that the sign problem is severe at almost all points in the phase diagram, with the exception of special cases like exactly zero chemical potential (ordinary QCD), which requires a particular order of limits. Part of our reasoning is based on the analyticity of free energy densities within their open phase regions. Finally, we describe a Monte Carlo technique to simulate finite-density QCD in regions where Z-/Z+ is small.