Anderson Localization in Quark-Gluon Plasma

TL;DR

This paper demonstrates that at high temperature, the low end of the quark-gluon plasma spectrum exhibits localized eigenstates with Poisson statistics, indicating a form of Anderson localization, contrasting with low-temperature behavior.

Contribution

It reveals a transition from localized Poisson-distributed eigenvalues to delocalized RMT-like statistics in high-temperature QCD spectra, highlighting Anderson localization phenomena.

Findings

Eigenvalues at high temperature are uncorrelated and follow Poisson statistics.

Eigenvectors at low spectrum are highly localized, becoming delocalized at higher energies.

Spectral statistics transition from Poisson to RMT-like with increasing eigenvalue.

Abstract

At low temperature the low end of the QCD Dirac spectrum is well described by chiral random matrix theory. In contrast, at high temperature there is no similar statistical description of the spectrum. We show that at high temperature the lowest part of the spectrum consists of a band of statistically uncorrelated eigenvalues obeying essentially Poisson statistics and the corresponding eigenvectors are extremely localized. Going up in the spectrum the spectral density rapidly increases and the eigenvectors become more and more delocalized. At the same time the spectral statistics gradually crosses over to the bulk statistics expected from the corresponding random matrix ensemble. This phenomenon is reminiscent of Anderson localization in disordered conductors. Our findings are based on staggered Dirac spectra in quenched SU(2) lattice simulations.