Effects of long-range hopping in the Bose-Hubbard model

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 we show that the Mott phase is shrunk in the parameters' space. We provide an exact solution for one-dimensional lattices and also two reliable approximations for higher dimensions. Finally, we extend these results to a more realistic situation in which long-range hopping is made by a combination of power-law and screening terms, studying the main effects on the Mott lobes.