  The extended Bose-Hubbard model captures the essential properties of a wide
variety of physical systems including ultracold atoms and molecules in optical
lattices, Josephson junction arrays, and certain narrow band superconductors.
It exhibits a rich phase diagram including a supersolid phase where a lattice
solid coexists with a superfluid. We use quantum Monte Carlo to study the
supersolid part of the phase diagram of the extended Bose-Hubbard model on the
simple cubic lattice. We add disorder to the extended Bose-Hubbard model and
find that the maximum critical temperature for the supersolid phase tends to be
suppressed by disorder. But we also find a narrow parameter window in which the
supersolid critical temperature is enhanced by disorder. Our results show that
supersolids survive a moderate amount of spatial disorder and thermal
fluctuations in the simple cubic lattice.
