Quantum chaos and chiral symmetry at the QCD and QED phase transition

TL;DR

This paper studies the eigenvalue spectra of Dirac operators in various gauge theories, revealing universal quantum chaotic behavior and random matrix theory descriptions across different phases and coupling regimes.

Contribution

It demonstrates that spectral correlations in lattice gauge theories follow random matrix theory predictions in both confined and chirally symmetric phases, extending understanding of quantum chaos in QCD and QED.

Findings

Bulk spectral correlations match random matrix theory predictions.

Low-lying Dirac spectra exhibit universal behavior consistent with random matrix theory.

Quantum chaos indicators are present across different phases of gauge theories.

Abstract

We investigate the eigenvalue spectrum of the staggered Dirac matrix in SU(3) gauge theory and in full QCD as well as in quenched U(1) theory. As a measure of the fluctuation properties of the eigenvalues, we consider the nearest-neighbor spacing distribution. We find that in all regions of their phase diagrams, compact lattice gauge theories have bulk spectral correlations given by random matrix theory, which is an indication for quantum chaos. In the confinement phase, the low-lying Dirac spectrum of these quantum field theories is well described by random matrix theory, exhibiting universal behavior. Related results for gauge theories with minimal coupling are now discussed also in the chirally symmetric phase.