A quantum Monte Carlo study of the long-ranged site-diluted XXZ-model as realized by polar molecules

Motivated by recent experiments with ultracold polar molecules trapped in deep optical lattices, we study ground-state properties of the long-ranged XXZ model with and without off-diagonal disorder. We map the spin model to a hard-core Bose-Hubbard model and perform large-scale Monte Carlo simulations by the Worm algorithm. In absence of disorder, we find that, for large enough interaction, three phases are stabilized: a superfluid phase, a checkerboard solid phase, only present at density n = 0.5, and a checkerboard supersolid phase which can be reached by doping the CB phase away from half-filling. In the presence of off-diagonal disorder and at fixed density n=0.5, we find that, unlike what observed in the case of short-range hopping, localization never occurs even for site dilution larger than the percolation threshold, and off-diagonal order, though strongly suppressed, persists for arbitrarily large values of site-dilution.