Strong-coupling study of spin-1 bosons in square and triangular optical lattice

We examine the superfluid-Mott insulator (SF-MI) transition of antiferromagnetically interacting spin-1 bosons trapped in a square or triangular optical lattice. We perform a strong-coupling expansion up to the third order in the transfer integral $t$ between the nearest-neighbor lattices. As expected from previous studies, an MI phase with an even number of bosons is considerably more stable against the SF phase than it is with an odd number of bosons. Results for the triangular lattice are similar to those for the square lattice, which suggests that the lattice geometry does not strongly affect the stability of the MI phase against the SF phase.