Solving the sign problems of the massless lattice Schwinger model with a dual formulation

TL;DR

This paper introduces a dual variable formulation of the massless lattice Schwinger model that eliminates the complex action problem, enabling unrestricted Monte Carlo simulations even with chemical potential or topological terms.

Contribution

The authors derive an exact dual representation of the lattice Schwinger model, transforming it into a form with only real and positive contributions.

Findings

Dual formulation removes sign problem

Enables Monte Carlo simulations with chemical potential

Allows studies of topological effects without restrictions

Abstract

We derive an exact representation of the massless Schwinger model on the lattice in terms of dual variables which are configurations of loops, dimers and plaquette occupation numbers. When expressed with the dual variables the partition sum has only real and positive terms also when a chemical potential or a topological term are added -- situations where the conventional representation has a complex action problem. The dual representation allows for Monte Carlo simulations without restrictions on the values of the chemical potential or the vacuum angle.