  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-Jz-Jperp
model, with Jperp=a Jz. Coexistence of superfluid hole-rich and insulating,
antiferromagnetically ordered hole-free phases is observed at sufficiently low
hole density, for any a < 1. A two-component checkerboard supersolid phase is
not observed. The experimental relevance and possible broader implications of
these findings are discussed.
