QCD Dirac operator at nonzero chemical potential: lattice data and matrix model

TL;DR

This paper compares lattice QCD data with a non-Hermitian matrix model to validate the model's predictions of Dirac eigenvalues at nonzero chemical potential, finding excellent agreement across regimes.

Contribution

It provides numerical evidence supporting the conjecture that the matrix model accurately describes the spectral correlations of the QCD Dirac operator at nonzero chemical potential.

Findings

Excellent agreement between lattice data and matrix model predictions.

Validation of the matrix model in both weak and strong non-Hermiticity regimes.

Supports the use of the matrix model for studying QCD eigenvalue spectra.

Abstract

Recently, a non-Hermitian chiral random matrix model was proposed to describe the eigenvalues of the QCD Dirac operator at nonzero chemical potential. This matrix model can be constructed from QCD by mapping it to an equivalent matrix model which has the same symmetries as QCD with chemical potential. Its microscopic spectral correlations are conjectured to be identical to those of the QCD Dirac operator. We investigate this conjecture by comparing large ensembles of Dirac eigenvalues in quenched SU(3) lattice QCD at nonzero chemical potential to the analytical predictions of the matrix model. Excellent agreement is found in the two regimes of weak and strong non-Hermiticity, for several different lattice volumes.