Universal spectral correlations of the Dirac operator at finite temperature

TL;DR

This paper analyzes the spectral correlations of the Dirac operator at finite temperature using advanced mathematical methods, revealing that microscopic correlations retain their form when scaled appropriately with temperature-dependent parameters.

Contribution

It extends the understanding of spectral correlations at finite temperature by deriving universal results applicable across different temperature regimes.

Findings

Microscopic spectral correlations match zero-temperature form after rescaling.

Results are valid on both mean level spacing and microscopic scales.

The spectral correlation functions are universal when scaled by the temperature-dependent chiral condensate.

Abstract

Using the graded eigenvalue method and a recently computed extension of the Itzykson-Zuber integral to complex matrices, we compute the $k$-point spectral correlation functions of the Dirac operator in a chiral random matrix model with a deterministic diagonal matrix added. We obtain results both on the scale of the mean level spacing and on the microscopic scale. We find that the microscopic spectral correlations have the same functional form as at zero temperature, provided that the microscopic variables are rescaled by the temperature-dependent chiral condensate.