Strong-coupling perturbation theory for the two-dimensional Bose-Hubbard model in a magnetic field

TL;DR

This paper develops a strong-coupling perturbation theory for the 2D Bose-Hubbard model in a magnetic field, revealing altered phase diagrams and qualitative agreement with experiments on Josephson-junction arrays.

Contribution

It introduces a novel application of strong-coupling perturbation theory to the Bose-Hubbard model under magnetic fields, extending understanding of phase behavior.

Findings

Phase diagram shapes change with magnetic field.

Altered phase lobes from zero-field behavior.

Qualitative agreement with Josephson-junction array experiments.

Abstract

The Bose-Hubbard model in an external magnetic field is investigated with strong-coupling perturbation theory. The lowest-order secular equation leads to the problem of a charged particle moving on a lattice in the presence of a magnetic field, which was first treated by Hofstadter. We present phase diagrams for the two-dimensional square and triangular lattices, showing a change in shape of the phase lobes away from the well-known power-law behavior in zero magnetic field. Some qualitative agreement with experimental work on Josephson-junction arrays is found for the insulating phase behavior at small fields.