Imprints of $U_A(1)$ chiral anomaly and disorder in the Dirac eigenspectrum of QCD at finite temperature

TL;DR

This study investigates the Dirac eigenvalue spectrum in finite-temperature QCD, revealing how disorder and chiral symmetry restoration influence spectral properties and eigenvector structure, with implications for understanding the $U_A(1)$ anomaly.

Contribution

It provides the first calculation of Thouless conductance in the Dirac spectrum and links spectral features to chiral symmetry restoration and disorder effects.

Findings

Intermediate level statistics are identified in the Dirac spectrum.

Disorder correlates with the effective restoration of $U_A(1)$ symmetry.

Thouless conductance quantifies eigenvector rigidity and disorder effects.

Abstract

We perform a comprehensive study of the properties of Dirac eigenvalue spectrum in QCD as a function of temperature on the lattice. In addition to effects due to interplay between interactions and disorder inherently present in a many-body system, the Dirac spectrum also contains crucial information about the effective restoration of different subgroups of almost exact two-flavor chiral symmetry in QCD. We calculate the infrared eigenvalues of the overlap Dirac operator on 2+1 flavor QCD ensembles generated using domain wall fermion discretization, on a large volume lattice. From the normalized level spacing ratios, we identify those eigenvalues that have intermediate level statistics, distinctly different from the majority in the bulk spectrum that follow universal level fluctuations similar to a random matrix of Gaussian unitary type. We provide an explanation of these intermediate level ratios in terms of a specific random matrix model and quantify the correlation between these eigenstates and disorder in the gauge fields manifested in the renormalized Polyakov loop values. Whereas the existence of intermediate eigenmodes is intimately connected to the effective restoration of different subgroups of chiral symmetry close to chiral crossover transition, their origin can be traced to random uncorrelated disorder at higher temperatures when the $U_A(1)$ is effectively restored. We also, for the first time, calculate the Thouless conductance for the Dirac spectrum that quantifies the structural rigidity of the eigenvectors, and use it as a diagnostic tool to understand the restoration of the anomalous $U_A(1)$ subgroup of chiral symmetry and localization driven by disorder.