Momentum distribution of the insulating phases of the extended Bose-Hubbard model

We develop two methods to calculate the momentum distribution of the insulating (Mott and charge-density-wave) phases of the extended Bose-Hubbard model with on-site and nearest-neighbor boson-boson repulsions on d -dimensional hypercubic lattices. First, we construct the random-phase approximation result, which corresponds to the exact solution for the infinite-dimensional limit. Then, we perform a power-series expansion in the hopping t via strong-coupling perturbation theory, to evaluate the momentum distribution in two and three dimensions; we also use the strong-coupling theory to verify the random-phase approximation solution in infinite dimensions. Finally, we briefly discuss possible implications of our results in the context of ultracold dipolar Bose gases with dipole-dipole interactions loaded into optical lattices.