Anderson localization through Polyakov loops: lattice evidence and Random matrix model

TL;DR

This paper provides lattice evidence that local Polyakov loop fluctuations induce Anderson localization of low-lying fermion modes in SU(2) gauge theory, supported by a random matrix model that captures these effects.

Contribution

It demonstrates the role of Polyakov loop fluctuations in fermion localization and introduces a sparse random matrix model to reproduce observed phenomena.

Findings

Localization correlates with Polyakov loop fluctuations.

Transition from chaotic to integrable spectral behavior.

Random matrix model successfully mimics localization features.

Abstract

We investigate low-lying fermion modes in SU(2) gauge theory at temperatures above the phase transition. Both staggered and overlap spectra reveal transitions from chaotic (random matrix) to integrable (Poissonian) behavior accompanied by an increasing localization of the eigenmodes. We show that the latter are trapped by local Polyakov loop fluctuations. Islands of such "wrong" Polyakov loops can therefore be viewed as defects leading to Anderson localization in gauge theories. We find strong similarities in the spatial profile of these localized staggered and overlap eigenmodes. We discuss possible interpretations of this finding and present a sparse random matrix model that reproduces these features.