Solving the sign problem of two flavor scalar electrodynamics at finite chemical potential

TL;DR

This paper introduces a dual variable approach and a novel surface worm algorithm to exactly solve the complex phase problem in two-flavor scalar electrodynamics at finite chemical potential, enabling detailed phase diagram analysis.

Contribution

The paper develops a dual variable formulation and a new surface worm algorithm to efficiently simulate scalar electrodynamics with a complex phase problem at finite chemical potential.

Findings

Successful implementation of dual variables to solve the complex phase problem.

Development and testing of the surface worm algorithm for gauge-Higgs models.

Results showing the phase diagram and condensation phenomena in the model.

Abstract

We explore two flavor scalar electrodynamics on the lattice, which has a complex phase problem at finite chemical potential. By rewriting the action in terms of dual variables this complex phase problem can be solved exactly. The dual variables are link- and plaquette occupation numbers, subject to local constraints that have to be respected by the Monte Carlo algorithm. For the simulation we use a local update as well as the newly developed "surface worm algorithm", which is a generalization of the Prokof'ev Svistunov worm algorithm concept for simulating the dual representation of abelian Gauge-Higgs models on a lattice. We assess the performance of the two algorithms, present results for the phase diagram and discuss condensation phenomena.