High temperature quark localization by Polyakov loops

TL;DR

This paper investigates localized quark modes at high temperature, linking them to gauge field objects and Polyakov loop fluctuations, and introduces a random matrix model to explain spectral transitions.

Contribution

It reveals the connection between localized quark modes and gauge field fluctuations, and develops a random matrix model inspired by dimensional reduction.

Findings

Localized modes obey Poisson statistics

Modes are correlated with Polyakov loop fluctuations

Model reproduces spectral transition from Poisson to RMT

Abstract

We study the low eigenmodes of the overlap and staggered Dirac operator at high temperature. We show that the recently found localized quark modes obeying Poisson statistics are connected to physical gauge field objects with their size and density scaling in the continuum limit. The localized modes are also strongly correlated with large fluctuations of the Polyakov loop. Based on that we construct a random matrix model of the low Dirac modes inspired by dimensional reduction. Our model reproduces the Poisson to random matrix transition seen in the lattice Dirac spectrum.