Surface worm algorithm for abelian Gauge-Higgs systems on the lattice

TL;DR

This paper introduces the surface worm algorithm (SWA), a novel extension of the worm algorithm for lattice abelian Gauge-Higgs models, improving efficiency especially in dual representations with sign problems.

Contribution

The paper presents the surface worm algorithm (SWA), a new method for simulating abelian Gauge-Higgs models on lattices, extending the worm algorithm to surface and loop systems in dual form.

Findings

SWA outperforms local updates across various parameters.

SWA overcomes sign problems in dual representations.

Efficient sampling of surface and loop configurations.

Abstract

The Prokof'ev Svistunov worm algorithm was originally developed for models with nearest neighbor interactions that in a high temperature expansion are mapped to systems of closed loops. In this work we present the surface worm algorithm (SWA) which is a generalization of the worm algorithm concept to abelian Gauge-Higgs models on a lattice which can be mapped to systems of surfaces and loops (dual representation). Using Gauge-Higgs models with gauge groups Z(3) and U(1) we compare the SWA to the conventional approach and to a local update in the dual representation. For the Z(3) case we also consider finite chemical potential where the conventional representation has a sign problem which is overcome in the dual representation. For a wide range of parameters we find that the SWA clearly outperforms the local update.