Mott transition and spin structures of spin-1 bosons in two-dimensional optical lattice at unit filling

We study the ground state properties of spin-1 bosons in a two-dimensional optical lattice by applying a variational Monte Carlo method to the S = 1 Bose-Hubbard model on a square lattice at unit filling. A doublon-holon binding factor introduced in the trial state provides a noticeable improvement in the variational energy over the conventional Gutzwiller wave function and allows us to effectively deal with the intersite correlations of particle densities and spins. We systematically show how spin-dependent interactions modify the superfluid-Mott insulator transitions in the S = 1 Bose-Hubbard model owing to the interplay between the density and spin fluctuations of bosons. Furthermore, regarding the magnetic phases in the Mott region, the calculated spin structure factor elucidates the emergence of nematic and ferromagnetic spin orders for antiferromagnetic (U2> 0) and ferromagnetic (U2< 0) couplings, respectively.