We study by quantum Monte Carlo simulations the phase diagram of lattice hard-core bosons with nearest-neighbor repulsive interactions, in the presence of a superlattice of adsorption sites. For a moderate adsorption strength, the system forms crystal phases registered with the adsorption lattice; a “supersolid” phase exists, on both the vacancy and interstitial sides, whereas at commensuration, the superfluid density vanishes. The possible relevance of these results to experiments on ${}^4\text{H}\text{e}$ films adsorbed on graphite is discussed.

• Received 8 March 2010

DOI:https://doi.org/10.1103/PhysRevB.81.224502