Strong-coupling expansions for the topologically inhomogeneous Bose-Hubbard model

TL;DR

This paper develops third-order strong coupling perturbative expansions for the Bose-Hubbard model with arbitrary hopping, revealing new terms from triangular loops and inhomogeneities, and analyzing their effects on the insulating phase boundary.

Contribution

It introduces novel third-order perturbative terms accounting for inhomogeneous hopping and triangular loops in the Bose-Hubbard model, extending understanding of phase boundaries.

Findings

New terms from triangular loops and inhomogeneities identified

Inhomogeneities affect local boson density at first order

Results applicable to ultracold bosons in complex potentials

Abstract

We consider a Bose-Hubbard model with an arbitrary hopping term and provide the boundary of the insulating phase thereof in terms of third-order strong coupling perturbative expansions for the ground state energy. In the general case two previously unreported terms occur, arising from triangular loops and hopping inhomogeneities, respectively. Quite interestingly the latter involves the entire spectrum of the hopping matrix rather than its maximal eigenpair, like the remaining perturbative terms. We also show that hopping inhomogeneities produce a first order correction in the local density of bosons. Our results apply to ultracold bosons trapped in confining potentials with arbitrary topology, including the realistic case of optical superlattices with uneven hopping amplitudes. Significant examples are provided. Furthermore, our results can be extented to magnetically tuned transitions in Josephson junction arrays.