Higher-charge three-dimensional compact lattice Abelian-Higgs models

TL;DR

This paper studies three-dimensional lattice Abelian-Higgs models with higher scalar charges, revealing complex phase diagrams with multiple phases and phase transitions influenced by charge and component number, supported by Monte Carlo simulations.

Contribution

It introduces a detailed analysis of higher-charge Abelian-Higgs models, highlighting their richer phase structure compared to unit-charge models, with numerical validation.

Findings

Three distinct phases related to scalar condensation and confinement.

Phase transition features depend on charge q and component number N.

Numerical results for N=2 and N=25 support the proposed phase diagram scenario.

Abstract

We consider three-dimensional higher-charge multicomponent lattice Abelian-Higgs (AH) models, in which a compact U(1) gauge field is coupled to an N-component complex scalar field with integer charge q, so that they have local U(1) and global SU(N) symmetries. We discuss the dependence of the phase diagram, and the nature of the phase transitions, on the charge q of the scalar field and the number N>1 of components. We argue that the phase diagram of higher-charge models presents three different phases, related to the condensation of gauge-invariant bilinear scalar fields breaking the global SU(N) symmetry, and to the confinement/deconfinement of external charge-one particles. The transition lines separating the different phases show different features, which also depend on the number N of components. Therefore, the phase diagram of higher-charge models substantially differs from that of unit-charge models, which undergo only transitions driven by the breaking of the global SU(N) symmetry, while the gauge correlations do not play any relevant role. We support the conjectured scenario with numerical results, based on finite-size scaling analyses of Monte Carlo simuations for doubly-charged unit-length scalar fields with small and large number of components, i.e. N=2 and N=25.