The effective U(1)-Higgs theory at strong coupling on optical lattices?

TL;DR

This paper explores the strong coupling regime of the U(1)-Higgs model in two dimensions, aiming to connect it with Bose-Hubbard models on optical lattices, and discusses potential experimental implementations with cold atoms.

Contribution

It proposes a method to relate the U(1)-Higgs model at strong coupling to Bose-Hubbard models for optical lattice experiments.

Findings

Effective theory with integrated link variables and 4-field operators.

Restoration of plaquette interactions via order-by-order expansion.

Discussion of implementing the O(2) model with cold atom mixtures.

Abstract

We discuss the U(1)-Higgs model in two dimensions in the strongly coupled regime. If we neglect the plaquette interactions, we generate an effective theory where link variables are integrated out, producing 4-field operators. Plaquette interactions can be restored order by order as in recent calculations with staggered fermions. In the case of a SU(2) gauge theory with fermions, this strong coupling expansion can be related to the strong coupling expansion of Fermi-Hubbard models possibly implementable on optical lattice. We would like to provide a similar construction relating the U(1)-Higgs model to some Bose-Hubbard model. As a first step in this direction, we discuss a recent proposal to implement the O(2) model on optical lattices using a 87Rb and 41K Bose-Bose mixture of cold atoms.