Universality of Correlation Functions in Random Matrix Models of QCD

TL;DR

This paper proves that the microscopic spectral correlation functions in a QCD-inspired random matrix model remain universal even when a deterministic matrix breaks unitary invariance, across different temperatures.

Contribution

It demonstrates the universality of spectral correlation functions in a QCD-inspired random matrix model with a deterministic temperature-dependent part.

Findings

Universality holds even with broken unitary invariance.

Analytic calculation of correlation functions at arbitrary temperature.

Reproduction of the Laguerre kernel at zero temperature.

Abstract

We demonstrate the universality of the spectral correlation functions of a QCD inspired random matrix model that consists of a random part having the chiral structure of the QCD Dirac operator and a deterministic part which describes a schematic temperature dependence. We calculate the correlation functions analytically using the technique of Itzykson-Zuber integrals for arbitrary complex super-matrices. An alternative exact calculation for arbitrary matrix size is given for the special case of zero temperature, and we reproduce the well-known Laguerre kernel. At finite temperature, the microscopic limit of the correlation functions are calculated in the saddle point approximation. The main result of this paper is that the microscopic universality of correlation functions is maintained even though unitary invariance is broken by the addition of a deterministic matrix to the ensemble.