Mean-field theory for Bose-Hubbard Model under a magnetic field

TL;DR

This paper uses mean field theory to analyze how an effective magnetic field influences the superfluid-insulator transition in cold bosons, revealing that the critical hopping strength increases with the magnetic field and relates to the Hofstadter butterfly bandwidth.

Contribution

It introduces a mean field theoretical framework to study the magnetic field's effect on the Mott transition in the Bose-Hubbard model, linking critical parameters to the Hofstadter spectrum.

Findings

Critical hopping strength increases with magnetic field.

Critical hopping correlates with Hofstadter butterfly bandwidth.

Magnetization and superfluid density are calculated within mean field theory.

Abstract

We consider the superfluid-insulator transition for cold bosons under an effective magnetic field. We investigate how the applied magnetic field affects the Mott transition within mean field theory and find that the critical hopping strength $(t/U)_c$, increases with the applied field. The increase in the critical hopping follows the bandwidth of the Hofstadter butterfly at the given value of the magnetic field. We also calculate the magnetization and superfluid density within mean field theory.