Phase of the Fermion Determinant for QCD at Finite Chemical Potential

TL;DR

This paper explores the phase factor of the fermion determinant in QCD at finite chemical potential, analyzing its impact on physical observables, phase structure, and proposing observables that mitigate the sign problem for simulations.

Contribution

It provides a detailed analysis of the phase factor's properties, compares phase diagrams, and introduces teflon plated observables to improve Monte Carlo calculations under severe sign problems.

Findings

Distribution of the phase is Gaussian with width ~ μ T √V

The phase factor affects the validity of the Banks-Casher formula

Teflon plated observables enable accurate Monte Carlo simulations despite the sign problem

Abstract

In this lecture we discuss various properties of the phase factor of the fermion determinant for QCD at nonzero chemical potential. Its effect on physical observables is elucidated by comparing the phase diagram of QCD and phase quenched QCD and by illustrating the failure of the Banks-Casher formula with the example of one-dimensional QCD. The average phase factor and the distribution of the phase are calculated to one-loop order in chiral perturbation theory. In quantitative agreement with lattice QCD results, we find that the distribution is Gaussian with a width $\sim \mu T \sqrt V$ (for $m_\pi \ll T \ll \Lambda_{\rm QCD}$). Finally, we introduce, so-called teflon plated observables which can be calculated accurately by Monte Carlo even though the sign problem is severe.