A study of the sign problem for lattice QCD with chemical potential

TL;DR

This paper investigates the sign problem in lattice QCD with chemical potential by analyzing the phase of the fermion determinant across various parameters, comparing numerical results with chiral perturbation theory predictions.

Contribution

It introduces an exact dimensional reduction method for the fermion determinant and applies it to study the sign problem in different regimes of lattice QCD.

Findings

The phase of the fermion determinant varies with temperature, quark mass, and volume.

Results align with chiral perturbation theory predictions.

The method provides insights into the severity of the sign problem across parameters.

Abstract

We study the expectation value of the phase of the fermion determinant for Wilson lattice fermions with chemical potential. We use quenched SU(3) ensembles and implement a recently proposed exact dimensional reduction of the fermion determinant. Ensembles at several temperatures below and above the phase transition are studied and we analyze the role of the quark mass, the temperature, the volume and the topological sectors. We compare our numerical results to predictions from chiral perturbation theory.