Effects of long range hopping in the Bose-Hubbard model

TL;DR

This paper studies how long-range hopping affects the quantum phase transition in the Bose-Hubbard model, revealing phase boundary shifts and providing exact and approximate solutions for different dimensions.

Contribution

It offers the first exact solution for 1D lattices with long-range hopping and extends the analysis to more realistic models with combined power law and exponential decay.

Findings

Mott phase is reduced by long-range hopping

Exact solution for 1D case

Approximate solutions for higher dimensions

Abstract

We investigate the effects of an extended Bose-Hubbard model with a long range hopping term on the Mott insulator-superfluid quantum phase transition. We consider the effects of a power law decaying hopping term and show that the Mott phase is shrinked in the parameters' space. We provide an exact solution for one dimensional lattices and then two approximations for higher dimensions, each one valid in a specific range of the power law exponent: a continuum approximation and a discrete one. Finally, we extend these results to a more realistic situation, where the long range hopping term is made by a power law factor and a screening exponential term and study the main effects on the Mott lobes.