Dual lattice simulation of the U(1) gauge-Higgs model at finite density - an exploratory proof-of-concept study

TL;DR

This paper introduces a dual lattice simulation approach for the U(1) gauge-Higgs model at finite density, overcoming the complex action problem and enabling exploration of phase transitions and condensation phenomena.

Contribution

It presents an exact dual representation and a generalized worm algorithm for simulating the model at finite chemical potential, a novel approach in this context.

Findings

Successfully mapped the model to a dual representation with real, positive weights.

Simulated the phase diagram and condensation phenomena at finite chemical potential.

Demonstrated the effectiveness of the dual approach in overcoming the complex action problem.

Abstract

The U(1) gauge-Higgs model with two flavors of opposite charge and a chemical potential is mapped exactly to a dual representation where matter fields correspond to loops of flux and the gauge fields are represented by surfaces. The complex action problem of the conventional formulation at finite chemical potential mu is overcome in the dual representation and the partition sum has only real and non-zero contributions. We simulate the model in the dual representation using a generalized worm algorithm, explore the phase diagram and study condensation phenomena at finite mu.