Quantum Monte Carlo study of the long-range 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 site-diluted long-ranged XXZ model. Site dilution results in 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 site dilution, we find that, for large enough interaction, three phases are stabilized: a superfluid phase, a checkerboard solid phase, only present at density m=0.5, and a checkerboard supersolid phase which can be reached by doping the CB phase away from half filling. In the presence site-dilution and at fixed density m=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, although strongly suppressed, persists for arbitrarily large values of site dilution.