Dipolar Bose-Hubbard model

We study a simple model of interacting bosons on $d$-dimensional cubic lattice whose dynamics conserves both total boson number and dipole moment. This provides framework in which several remarkable consequences conservation can be explored. As function chemical potential hopping strength, the tuned between gapped Mott insulating phases various types gapless condensates. The condensed phase realized at large strengths, we dub Bose-Einstein insulator, is particularly interesting: despite having Bose condensate, it insulating, being an compressible.