Symmetry Crossover Protecting Chirality in Dirac Spectra

TL;DR

This paper introduces a random matrix model that interpolates between GUE and chGUE, revealing symmetry crossover effects that protect chirality in Dirac spectra and connecting to QCD-like theories.

Contribution

It provides a detailed derivation of spectral densities and partition functions for the interpolating model using supersymmetry, linking random matrix theory to QCD in the epsilon-regime.

Findings

The model interpolates between GUE and chGUE at the hard edge.

Derived microscopic level density and partition functions.

Confirmed the non-uniform GUE limit affects the hard edge behavior.

Abstract

We consider a random matrix model in the hard edge limit (local spectral statistics at the origin in the limit of large matrix size) which interpolates between the Gaussian unitary ensemble (GUE) and the chiral Gaussian unitary ensemble (chGUE). We show that this model is equivalent to the low-energy limit of certain QCD-like theories in the epsilon-regime. Moreover, we present a detailed derivation of the microscopic level density as well as the partially quenched and unquenched partition functions. Some of these results have been announced in a former letter by us. Our derivation relies on the supersymmetry method and is performed here step by step. Additionally, we compute the chiral condensate and the pion condensate for the quenched as well as unquenched settings. We also investigate the limits to GUE and chGUE and confirm our conjecture that the non-uniformity of the GUE limit would carry over to the hard edge limit.