Ground state phase diagram of spin-1/2 bosons in a two-dimensional   optical lattice
  We study a two-species bosonic Hubbard model on a two-dimensional square lattice by means of quantum Monte Carlo simulations. In addition to the usual contact repulsive interactions between the particles, the Hamiltonian has an interconversion term which allows the transformation of two particles from one species to the other. The phases are characterized by their solid or superfluid properties and by their polarization, i.e. the difference in the populations. When inter-species interactions are smaller than the intra-species ones, the system is unpolarized, whereas in the opposite case the system is unpolarized in even Mott insulator lobes and polarized in odd Mott lobes and also in the superfluid phase. We show that in the latter case the transition between the Mott insulator of total density two and the superfluid can be either of second or first order depending on the relative values of the interactions, whereas the transitions are continuous in all other cases. 
L. de Forges de Parny, F. H\'ebert, V. G. Rousseau, R. T. Scalettar   and G. G. Batrouni
cond-mat.quant-gas