Monte Carlo simulation of abelian gauge-Higgs lattice models using dual representation

TL;DR

This paper develops a dual representation for abelian gauge-Higgs lattice models with Z(3) and U(1) groups, enabling Monte Carlo simulations at finite chemical potential without complex action issues.

Contribution

It introduces an exact dual mapping to surface and loop variables, allowing efficient Monte Carlo updates and overcoming the complex action problem in these models.

Findings

Demonstrates condensation phenomena at varying chemical potentials.

Validates the dual approach with Monte Carlo simulations.

Shows real and positive contributions at finite chemical potential.

Abstract

We study abelian gauge-Higgs models on the lattice and consider gauge groups Z(3) and U(1). For both cases the partition sums are mapped exactly to a dual representation where the degrees of freedom are surfaces for the gauge fields and loops of flux that may serve as boundaries for the surfaces represent the matter fields. Also at finite chemical potential the dual partition sums have only real and positive contributions and the complex action problem of the conventional representation is overcome in the dual approach. We apply a local Metropolis update for the dual degrees of freedom, as well as a generalization of the worm algorithm to bounded surfaces. Results that illustrate condensation phenomena as a function of chemical potential are discussed.