  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.
