Fluctuations, correlations and the sign problem in QCD

TL;DR

This paper investigates the distribution and correlations of the fermion determinant's phase in QCD at non-zero chemical potential, revealing a qualitative change in distribution and implications for lattice simulations.

Contribution

It provides a detailed analysis of the phase distribution and correlations in QCD at finite chemical potential using Chiral Perturbation Theory and 1D QCD models, highlighting a transition in distribution type.

Findings

Distribution of the phase shifts from Gaussian to Lorentzian as quark mass enters the Dirac spectrum

Some observables show weak correlation with the fermion determinant's phase despite the sign problem

Results have practical implications for lattice QCD simulations at finite density

Abstract

We study the distribution of the phase angle and the magnitude of the fermion determinant as well as its correlation with the chiral condensate and the baryon number for QCD at non-zero quark chemical potential. Results are derived to one-loop order in Chiral Perturbation Theory (ChPT), as well as by analytical and numerical calculations in QCD in one Euclidean dimension. We find a qualitative change of the distribution of the phase of the fermion determinant when the quark mass enters the spectrum of the Dirac operator: it changes from a periodicized Gaussian distribution to a periodicized Lorentzian distribution. We also explore the possibility that some observables remain weakly correlated with the phase of the fermion determinant even though the sign problem is severe. We discuss the practical implications of our findings on lattice simulations of QCD at non-zero baryon chemical potential.