Individual complex Dirac eigenvalue distributions from random matrix theory and comparison to quenched lattice QCD with a quark chemical potential

TL;DR

This paper derives analytical distributions for individual complex eigenvalues of the QCD Dirac operator at nonzero chemical potential using random matrix theory and confirms their accuracy by comparing with lattice QCD data.

Contribution

It provides the first detailed analytical description of individual complex Dirac eigenvalues at finite chemical potential and validates these results against lattice QCD simulations.

Findings

Excellent agreement between analytical and lattice data near the origin.

Analytical results apply to systems with similar symmetry classes.

Distributions are derived for both quenched and unquenched cases.

Abstract

We analyze how individual eigenvalues of the QCD Dirac operator at nonzero quark chemical potential are distributed in the complex plane. Exact and approximate analytical results for both quenched and unquenched distributions are derived from non-Hermitian random matrix theory. When comparing these to quenched lattice QCD spectra close to the origin, excellent agreement is found for zero and nonzero topology at several values of the quark chemical potential. Our analytical results are also applicable to other physical systems in the same symmetry class.