Eur. Phys. J. B (2012) 85: 76
https://doi.org/10.1140/epjb/e2012-20852-5

Regular Article

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

Department of Physics, KoçUniversity, Rumelifeneri Yolu, 34450 Sariyer, Istanbul, Turkey

^a e-mail: miskin@ku.edu.tr

Received: 19 October 2011
Received in final form: 16 January 2012
Published online: 27 February 2012

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.