Duals of lattice Abelian models with static determinant at finite density

TL;DR

This paper develops dual formulations for Abelian lattice gauge theories with static fermion determinants at finite temperature and density, enabling reliable Monte Carlo simulations due to positive weights and revealing new phase structures.

Contribution

It introduces a broad class of dual formulations for Abelian gauge theories with static determinants, valid across dimensions and flavors, with positive weights for finite density simulations.

Findings

Dual formulations have strictly positive Boltzmann weights.

An exact solution for the (1+1)-dimensional partition function is provided.

A phase with oscillating correlations is identified.

Abstract

Dual formulations of Abelian U(1) and Z(N) LGT with a static fermion determinant are constructed at finite temperatures and non-zero chemical potential. The dual form is valid for a broad class of lattice gauge actions, for arbitrary number of fermion flavors and in any dimension. The distinguished feature of the dual formulation is that the dual Boltzmann weight is strictly positive. This allows to gain reliable results at finite density via the Monte Carlo simulations. As a byproduct of the dual representation we outline an exact solution for the partition function of the (1 + 1)-dimensional theory and reveal an existence of a phase with oscillating correlations.