Deconfinement transition and localization of Dirac modes in finite-temperature $\mathbb{Z}_3$ gauge theory on the lattice

TL;DR

This paper investigates how Dirac eigenmodes localize across the deconfinement transition in a finite-temperature $ ext{Z}_3$ gauge theory, revealing limitations of existing localization models and proposing an improved theoretical framework.

Contribution

It demonstrates the presence of localized low modes in all Polyakov-loop sectors and introduces a refined localization model emphasizing spatial hopping effects.

Findings

Localized low modes are observed in all Polyakov-loop sectors.

The standard sea-islands picture has limitations, especially in complex sectors.

An improved localization model with enhanced spatial hopping explains the results well.

Abstract

We study the localization properties of the eigenmodes of the staggered Dirac operator across the deconfinement transition in finite-temperature $\mathbb{Z}_3$ pure gauge theory on the lattice in 2+1 dimensions. This allows for nontrivial tests of the sea-islands picture of localization, according to which low modes should localize on favorable Polyakov-loop fluctuations in the deconfined phase of a gauge theory. We observe localized low modes in the deconfined phase of the theory, both in the real Polyakov-loop sector, where they are expected, and in the complex Polyakov-loop sectors, where they are not. Our findings expose the limitations of the standard sea-islands picture, and call for its refinement. An improved picture, where spatial hopping terms play a more prominent role, is proposed and found to be in excellent agreement with numerical results.