Dual simulation of the 2-dimensional lattice U(1) gauge-Higgs model with a topological term

TL;DR

This paper develops a dual variable formulation for the 2D U(1) gauge-Higgs model with a topological term, enabling Monte Carlo simulations across all vacuum angles and exploring its phase structure.

Contribution

The authors introduce an exact dual representation that overcomes the complex action problem, allowing for efficient simulations of the model at arbitrary topological angles.

Findings

Successful dual simulation at various vacuum angles

Analysis of the continuum limit of the model

Mapping of the phase diagram of the system

Abstract

The 2-dimensional U(1) gauge-Higgs model with a topological term is a simple example of a lattice field theory where the complex action problem comes from the topological term. We show that the model can be exactly rewritten in terms of dual variables, such that the dual partition sum has only real and positive contributions. Using suitable algorithms the dual formulation allows for Monte Carlo simulations at arbitrary values of the vacuum angle. We demonstrate the feasibility of the dual simulation and study the continuum limit, as well as the phase diagram of the system.