Non-compact lattice Higgs model with Abelian discrete gauge groups: phase diagram and gauge symmetry enlargement

TL;DR

This paper explores the phase diagram of a three-dimensional lattice Higgs model with Abelian discrete gauge groups, revealing conditions for continuous phase transitions and symmetry enlargement to the Abelian Higgs universality class.

Contribution

It demonstrates that gauge symmetry enlargement occurs in the lattice Higgs model with discrete groups when certain conditions on group order and number of scalar fields are met.

Findings

Critical transitions are in orthogonal universality classes for small N.

Symmetry enlargement to Abelian Higgs occurs for q ≥ 5 and large N.

The model's phase diagram depends on the gauge group and scalar field number.

Abstract

We study the phase diagram and phase transitions of the three dimensional multicomponent lattice Higgs model with non-compact Abelian discrete groups. The model with non-compact U(1) gauge group is known to undergo, for a sufficiently large number of scalar fields $N$, a continuous transition associated to the charged fixed point of the continuous Abelian Higgs field theory. We show that in the model with gauge group $\mathbb{Z}_q^{(nc)}\equiv 2\pi\mathbb{Z}/q$ only critical transitions in the orthogonal universality classes are present for small values of $N$, while a symmetry enlargement to the continuous Abelian Higgs universality class happens when $q\ge 5$ and $N$ is large enough.