Numerical simulation of self-dual U(1) lattice field theory with electric and magnetic matter

TL;DR

This paper investigates a U(1) lattice field theory with electric and magnetic matter, using Monte Carlo simulations to analyze self-duality, phase transitions, and the effects of matter coupling on the system's symmetry.

Contribution

It introduces a duality-based formulation of U(1) lattice theory with electric and magnetic matter, and studies the spontaneous breaking of self-duality through numerical simulations.

Findings

Self-duality is spontaneously broken in a certain matter coupling interval.

Endpoints of the symmetry-breaking interval are identified.

A first order transition occurs when crossing the self-dual point.

Abstract

We study a recently proposed formulation of U(1) lattice field theory with electric and magnetic matter based on the Villain formulation. This discretization allows for a duality that gives rise to relations between weak and strong gauge coupling. There exists a self-dual value of the gauge coupling where one may study the model as a function of the remaining matter coupling. Using Monte Carlo simulations based on a worldline/worldsheet representation of the system we evaluate order parameters for spontaneous breaking of self-duality. We find that in some interval of the matter coupling self-duality becomes broken spontaneously. We determine the endpoints of this interval and study the nature of the corresponding critical points. Finally we explore the system away from the self-dual gauge coupling and show that when crossing the self-dual point a first order jump is seen in the order parameters.