Destruction of diagonal and off-diagonal long range order by disorder in   two-dimensional hard core boson systems
  We use quantum Monte Carlo simulations to study the effect of disorder, in the form of a disordered chemical potential, on the phase diagram of the hard core bosonic Hubbard model in two dimensions. We find numerical evidence that in two dimensions, no matter how weak the disorder, it will always destroy the long range density wave order (checkerboard solid) present at half filling and strong nearest neighbor repulsion and replace it with a bose glass phase. We study the properties of this glassy phase including the superfluid density, energy gaps and the full Green's function. We also study the possibility of other localized phases at weak nearest neighbor repulsion, i.e. Anderson localization. We find that such a phase does not truly exist: The disorder must exceed a threshold before the bosons (at weak nn repulsion) are localized. The phase diagram for hard core bosons with disorder cannot be obtained easily from the soft core phase diagram discussed in the literature. 
K. Bernardet, G. G. Batrouni, M. Troyer, A. Dorneich