Quantum chaos in supersymmetric QCD at finite density

TL;DR

This study explores quantum chaos in supersymmetric QCD at finite density by analyzing eigenvalue spacings of the lattice Dirac operator, revealing Wigner distribution at zero density and Ginibre ensemble behavior at finite density.

Contribution

It introduces a method to analyze eigenvalue spacings in complex spectra of the Dirac operator at finite density and compares results with non-hermitian random matrix theory.

Findings

Eigenvalue spacings follow Wigner distribution at zero chemical potential.

Eigenvalues become complex at nonzero chemical potential.

Agreement with Ginibre ensemble observed at moderate chemical potential.

Abstract

We investigate the distribution of the spacings of adjacent eigenvalues of the lattice Dirac operator. At zero chemical potential $\mu$, the nearest-neighbor spacing distribution $P(s)$ follows the Wigner surmise of random matrix theory both in the confinement and in the deconfinement phase. This is indicative of quantum chaos. At nonzero chemical potential, the eigenvalues of the Dirac operator become complex and we discuss how $P(s)$ can be defined in the complex plane. Numerical results from an SU(2) simulation with staggered fermions in fundamental and adjoint representations are compared with predictions from non-hermitian random matrix theory, and agreement with the Ginibre ensemble is found for $\mu\approx 0.5$.