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.