Localization of Dirac modes in a finite temperature SU(2) Higgs model

TL;DR

This study investigates the localization of low-lying Dirac modes in a finite-temperature SU(2) Higgs model, confirming the 'sea/islands' mechanism across different phases and transitions.

Contribution

It demonstrates that Dirac mode localization correlates with Polyakov loop ordering in the SU(2)-Higgs model, extending the 'sea/islands' localization picture beyond pure gauge theories.

Findings

Localization occurs in deconfined and Higgs phases

No localization in the confined phase

Supports the universality of the 'sea/islands' mechanism

Abstract

Low-lying Dirac modes become localized at the finite-temperature transition in QCD and other gauge theories, indicating a strong connection between localization and deconfinement. This phenomenon can be understood through the "sea/islands" picture: in the deconfined phase, modes become trapped on "islands" of Polyakov loop fluctuations within a "sea" of ordered Polyakov loops. To test the universality of the "sea/islands" mechanism, we investigate whether changes in the localization properties of low modes occur across other thermal transitions where the Polyakov loop becomes ordered, beyond the usual deconfinement transition. The fixed-length SU(2)-Higgs model is appropriate for this study. After mapping out the phase diagram, we find that low Dirac modes become localized in the deconfined and Higgs phases, where the Polyakov loop is ordered. However, localization is absent in the confined phase. These findings confirm the "sea/islands" picture of localization.