Chiral Random Matrix Model for Critical Statistics

TL;DR

This paper introduces a chiral random matrix model that captures the transition from universal chiral RMT behavior to critical statistics, effectively modeling QCD Dirac spectra in instanton liquid configurations.

Contribution

A novel chiral random matrix model that interpolates between chiral RMT and Poisson ensembles, describing critical spectral statistics in QCD.

Findings

Spectral correlations follow chiral RMT below a critical energy.

Number variance exhibits linear growth beyond the critical energy.

Model accurately describes QCD Dirac spectra in instanton liquid regimes.

Abstract

We propose a random matrix model that interpolates between the chiral random matrix ensembles and the chiral Poisson ensemble. By mapping this model on a non-interacting Fermi-gas we show that for energy differences less than a critical energy $E_c$ the spectral correlations are given by chiral Random Matrix Theory whereas for energy differences larger than $E_c$ the number variance shows a linear dependence on the energy difference with a slope that depends on the parameters of the model. If the parameters are scaled such that the slope remains fixed in the thermodynamic limit, this model provides a description of QCD Dirac spectra in the universality class of critical statistics. In this way a good description of QCD Dirac spectra for gauge field configurations given by a liquid of instantons is obtained.