Effect of anisotropic hopping on the Bose Hubbard model phase diagram: strong-coupling perturbation theory on a square lattice

TL;DR

This paper investigates how anisotropic hopping in the Bose Hubbard model influences its phase diagram, revealing minor effects for weak anisotropy and potential dimensional crossover at strong anisotropy using strong-coupling perturbation theory.

Contribution

It provides a detailed analysis of the impact of hopping anisotropy on the phase diagram of the Bose Hubbard model, highlighting the effects of varying anisotropy strength.

Findings

Weak anisotropy slightly modifies the phase diagram.

Strong anisotropy may lead to dimensional crossover effects.

The study uses strong-coupling perturbation theory on a square lattice.

Abstract

There has been a recent resurgence of experimental efforts to quantitatively determine the phase diagram of the Bose Hubbard model by carefully analyzing experiments with ultracold bosonic atoms on an optical lattice. In many realizations of these experiments, the hopping amplitudes are not homogeneous throughout the lattice, but instead, the lattice has an anisotropy where hopping along one direction is not exactly equal to hopping along a perpendicular direction. In this contribution, we examine how an anisotropy in the hopping matrix elements affects the Mott lobes of the Bose Hubbard model. For weak anisotropy, we find the phase diagram is only slightly modified when expressed in terms of the average hopping, while for strong anisotropy, one expects to ultimately see dimensional crossover effects.