Dual representation for massless fermions with chemical potential and U(1) gauge fields

TL;DR

This paper develops a dual representation for massless fermions with U(1) gauge fields, including topological terms and chemical potential, enabling Monte Carlo simulations by ensuring real and positive contributions.

Contribution

It introduces a generalized dualization method for massless fermions with topological terms and chemical potential, applicable to nanowire systems coupled to higher-dimensional gauge fields.

Findings

Dual representation yields real and positive weights for simulations.

Method extends to nanowire systems in higher dimensions.

Facilitates Monte Carlo studies of complex fermionic systems.

Abstract

Complex action problems coming from either a chemical potential or a topological term have been solved for several models in recent years by mapping them to so-called dual degrees of freedom. In terms of these dual variables the partition sum has only real and positive contributions such that a Monte Carlo simulation is possible. In this paper we discuss a dual representation for massless staggered fermions in two dimensions coupled to a U(1) gauge field. We include a topological term, and for the case of several flavors with vanishing total charge also a chemical potential. We show that the real and positive dualization can also be generalized to a system of nanowires (1+1 dimensional fermions) coupled to a 3+1 dimensional U(1) gauge field.