Phase diagram of two-component bosons on an optical lattice

We present a theoretical analysis of the phase diagram of two-component bosons on an optical lattice. A new formalism is developed which treats the effective spin interactions in the Mott and superfluid phases on the same footing. Using this new approach we chart the phase boundaries of the broken spin symmetry states up to the Mott to superfluid transition and beyond. Near the transition point, the magnitude of spin exchange can be very large, which facilitates the experimental realization of spin-ordered states. We find that spin and quantum fluctuations have a dramatic effect on the transition, making it first order in extended regions of the phase diagram. When each species is at integer filling, an additional phase transition may occur, from a spin-ordered insulator to a Mott insulator with no broken symmetries. We determine the phase boundaries in this regime and show that this is essentially a Mott transition in the spin sector.