Localization properties of Dirac modes at the Roberge-Weiss phase transition

TL;DR

This paper investigates how low-lying Dirac eigenmodes in QCD become localized or delocalized across the Roberge-Weiss transition, revealing a link between localization and deconfinement in a model with a genuine transition.

Contribution

It demonstrates for the first time in a continuum limit model with dynamical fermions that the localization of Dirac modes is connected to the deconfinement transition at the Roberge-Weiss point.

Findings

Modes are localized below a temperature-dependent mobility edge.

The mobility edge vanishes at the Roberge-Weiss transition temperature.

Localization of Dirac modes correlates with deconfinement.

Abstract

We study the localization properties of the low-lying Dirac eigenmodes in QCD at imaginary chemical potential $\hat{\mu}_I=\pi$ at temperatures above the Roberge-Weiss transition temperature $T_{\rm RW}$. We find that modes are localized up to a temperature-dependent "mobility edge" and delocalized above it, and that the mobility edge extrapolates to zero at a temperature compatible with $T_{\rm RW}$. This supports the existence of a strong connection between localization of the low Dirac modes and deconfinement, studied here for the first time in a model with a genuine deconfinement transition in the continuum limit in the presence of dynamical fermions.