Phase diagram of an anisotropic bosonic t-J model

We have studied by quantum Monte Carlo simulations the low temperature phase diagram of a mixture of isotopic, hard core bosons, described by the t-J(z)-J(perpendicular to) model, with J(perpendicular to) = alpha J(z). The coexistence of superfluid hole-rich and insulating, antiferromagnetically ordered hole-free phases is observed at sufficiently low hole density for any alpha<1. A two-component checkerboard supersolid phase is not observed. The experimental relevance and possible broader implications of these findings are discussed.