Strong-coupling perturbation theory for the extended Bose-Hubbard model

We develop a strong-coupling perturbation theory for the extended Bose-Hubbard model with on-site and nearest-neighbor boson-boson repulsions on (\$d > 1\$)-dimensional hypercubic lattices. Analytical expressions for the ground-state phase boundaries between the incompressible (Mott or charge-density-wave insulators) and the compressible (superfluid or supersolid) phases are derived up to third order in the hopping \$t\$. We also briefly discuss possible implications of our results in the context of ultracold dipolar Bose gases with dipole-dipole interactions loaded into optical lattices.