Magnetic phases and transitions of the two-species Bose-Hubbard model

A model of two-species bosons moving on the sites of a lattice is studied at nonzero temperature, focusing on magnetic order and superfluid-insulator transitions. Firstly, Landau theory is used to find the general structure of the phase diagram, and in particular to demonstrate the presence of first-order transitions and hysteresis in the vicinity of a multicritical point. Secondly, an explicit thermodynamic phase diagram is calculated using an approach based on a field-theoretical description of the Bose-Hubbard model, which incorporates the crucial effects of particle-number fluctuations. The maximum transition temperature to a magnetically ordered Mott insulator is found to be limited by the presence of the superfluid phase.