Artificial gauge fields for the Bose-Hubbard model on a checkerboard superlattice and extended Bose-Hubbard model

TL;DR

This paper investigates how artificial gauge fields influence the phase transitions in the two-dimensional Bose-Hubbard model on a checkerboard superlattice, revealing flux-independent energy gaps and deriving analytical phase boundary expressions.

Contribution

It provides the first analytical mean-field expressions for superfluid-insulator phase boundaries in this specific lattice with gauge fields, and relates findings to the extended Bose-Hubbard model.

Findings

Checkerboard superlattice induces flux-independent energy gaps.

Derived analytical phase transition boundaries for superfluid-Mott insulator.

Commented on magnetic field effects on extended Bose-Hubbard model.

Abstract

We study the effects of an artificial gauge field on the ground-state phases of the Bose-Hubbard model on a checkerboard superlattice in two dimensions, including the superfluid phase and the Mott and alternating Mott insulators. First, we discuss the single-particle Hofstadter problem, and show that the presence of a checkerboard superlattice gives rise to a magnetic flux-independent energy gap in the excitation spectrum. Then, we consider the many-particle problem, and derive an analytical mean-field expression for the superfluid-Mott and superfluid--alternating-Mott insulator phase transition boundaries. Finally, since the phase diagram of the Bose-Hubbard model on a checkerboard superlattice is in many ways similar to that of the extended Bose-Hubbard model, we comment on the effects of magnetic field on the latter model, and derive an analytical mean-field expression for the superfluid-insulator phase transition boundaries as well.