Matrix model correlation functions and lattice data for the QCD Dirac operator with chemical potential

TL;DR

This paper uses a complex chiral random matrix model to analyze QCD with small chemical potential, deriving eigenvalue correlations analytically and validating them against lattice QCD data, revealing two distinct scaling regimes.

Contribution

It introduces an effective complex matrix model for QCD at small chemical potential and analytically determines eigenvalue correlations in different regimes, validated by lattice data.

Findings

Confirmation of two different scaling regimes in lattice data

Analytical eigenvalue correlation functions derived for weak and strong non-Hermiticity

Good agreement between model predictions and lattice data

Abstract

We apply a complex chiral random matrix model as an effective model to QCD with a small chemical potential at zero temperature. In our model the correlation functions of complex eigenvalues can be determined analytically in two different limits, at weak and strong non-Hermiticity. We compare them to the distribution of the smallest Dirac operator eigenvalues from quenched QCD lattice data for small values of the chemical potential, appropriately rescaled with the volume. This confirms the existence of two different scaling regimes from lattice data.