Localization of Dirac modes in the $\mathrm{SU}(2)$ Higgs model at finite temperature

TL;DR

This study explores how low-lying Dirac modes localize in the SU(2) Higgs model at finite temperature, revealing their dependence on phase transitions and Polyakov-loop ordering.

Contribution

It provides the first detailed analysis of Dirac mode localization in the SU(2) Higgs model, connecting localization properties with phase structure and Polyakov-loop behavior.

Findings

Localized low modes in deconfined and Higgs phases

Disappearance of localized modes in the confined phase

Supports the 'sea/islands' localization picture

Abstract

We investigate the connection between localization of low-lying Dirac modes and Polyakov-loop ordering in the lattice $\mathrm{SU}(2)$ Higgs model at finite temperature, probed with the staggered Dirac operator. After mapping out the phase diagram of the model at a fixed temporal extension in lattice units, we study the localization properties of the low-lying modes of the staggered Dirac operator, how these properties change across the various transitions, and how these modes correlate with the gauge and Higgs fields. We find localized low modes in the deconfined and in the Higgs phase, where the Polyakov loop is strongly ordered, but in both cases they disappear as one crosses over to the confined phase. Our findings confirm the general expectations of the "sea/islands" picture, and the more detailed expectations of its refined version concerning the favorable locations of localized modes, also in the presence of dynamical scalar matter.