Level spacings for weakly asymmetric real random matrices and application to two-color QCD with chemical potential

TL;DR

This paper studies how eigenvalue spacings in real symmetric matrices are affected by antisymmetric perturbations, with applications to two-color QCD, providing analytical surmises validated for large matrices.

Contribution

It introduces analytical surmises for level spacings in perturbed real symmetric matrices and demonstrates their applicability to two-color QCD with chemical potential.

Findings

Analytical formulas accurately describe level spacings in large matrices.

Level spacings are consistent with symmetry-based expectations.

Results apply to the overlap Dirac operator in two-color QCD.

Abstract

We consider antisymmetric perturbations of real symmetric matrices in the context of random matrix theory and two-color quantum chromodynamics. We investigate the level spacing distributions of eigenvalues that remain real or become complex conjugate pairs under the perturbation. We work out analytical surmises from small matrices and show that they describe the level spacings of large random matrices. As expected from symmetry arguments, these level spacings also apply to the overlap Dirac operator for two-color QCD with chemical potential.