Phase of the Fermion Determinant at Nonzero Chemical Potential

TL;DR

This paper investigates the behavior of the fermion determinant's phase in QCD at nonzero chemical potential, showing it remains nonzero below a critical value and is exponentially suppressed above it, using chiral Lagrangian and random matrix models.

Contribution

It provides explicit expressions for the average phase factor in the microscopic domain of QCD at nonzero chemical potential, linking chiral Lagrangian and random matrix theory.

Findings

Average phase factor is nonzero for μ < m_π/2

Exponential suppression of phase factor for larger μ

Derived explicit formulas using random matrix theory

Abstract

We show that in the microscopic domain of QCD (also known as the $\epsilon$-domain) at nonzero chemical potential the average phase factor of the fermion determinant is nonzero for $\mu < m_\pi/2$ and is exponentially suppressed for larger values of the chemical potential. This follows from the chiral Lagrangian that describes the low-energy limit of the expectation value of the phase factor. Explicit expressions for the average phase factor are derived using a random matrix formulation of the zero momentum limit of this chiral Lagrangian.