Quantum and Thermal Transitions Out of the Pair-Supersolid Phase of Two-Species Bosons in Lattice

We investigate two-species bosons in a two-dimensional square lattice by quantum Monte Carlo method. We show that the inter-species attraction and nearest-neighbor intra-species repulsion results in the pair-supersolid phase, where a diagonal solid order coexists with an off-diagonal pair-superfluid order. The quantum and thermal transitions out of the pair-supersolid phase are characterized. It is found that there is a direct first order transition from the pair-supersolid phase to the double-superfluid phase without an intermediate region. Furthermore, the melting of the pair-supersolid occurs in two steps. Upon heating, first the pair-superfluid is destroyed via a KT transition then the solid order melts via an Ising transition