Center vortices and localized Dirac modes in the deconfined phase of (2+1)-dimensional lattice $\mathbb{Z}_2$ gauge theory

TL;DR

This paper investigates the deconfinement transition in (2+1)-dimensional lattice $ ext{Z}_2$ gauge theory, linking center vortex percolation with localization of Dirac modes and analyzing critical phenomena.

Contribution

It provides a detailed analysis of the Anderson transition in the Dirac spectrum and the vortex percolation transition, highlighting their distinct critical behaviors and the relation to mode localization.

Findings

The Anderson transition in the Dirac spectrum is of BKT type.

Center-vortex percolation differs from ordinary 2D percolation.

Localized Dirac modes are supported by simple vortex structures.

Abstract

We study the deconfinement transition in (2+1)-dimensional lattice $\mathbb{Z}_2$ gauge theory both as a percolation transition of center vortices and as a localization transition for the low-lying Dirac modes. We study in detail the critical properties of the Anderson transition in the Dirac spectrum in the deconfined phase, showing that it is of BKT type; and the critical properties of the center-vortex percolation transition, showing that they differ from those of ordinary two-dimensional percolation. We then study the relation between localized modes and center vortices in the deconfined phase, identifying the simple center-vortex structures that mainly support the localized Dirac modes. As the system transitions to the confined phase, center vortices merge together into an infinite cluster, causing the low Dirac modes to delocalize.