Two-Dimensional Bose-Hubbard Model For Helium On Graphene

An exciting development in the field of correlated systems is the possibility of realizing two-dimensional (2D) phases of quantum matter. For a system of bosons, an example of strong correlations manifesting themselves in a 2D environment is provided by helium adsorbed on graphene. We construct the effective Bose-Hubbard model for this system which involves hard-core bosons (U approximate to infinity), repulsive nearest-neighbor (V > 0) and small attractive (V' < 0) next-nearest-neighbor interactions. The mapping onto the Bose-Hubbard model is accomplished by a variety of many-body techniques which take into account the strong He-He correlations on the scale of the graphene lattice spacing. Unlike the case of dilute ultracold atoms where interactions are effectively pointlike, the detailed microscopic form of the short-range electrostatic and long-range dispersion interactions in the helium-graphene system is crucial for the emergent Bose-Hubbard description. The result places the ground state of the first layer of He-4 adsorbed on graphene deep in the commensurate solid phase with 1/3 of the sites on the dual triangular lattice occupied. Because the parameters of the effective Bose-Hubbard model are very sensitive to the exact lattice structure, this opens up an avenue to tune quantum phase transitions in this solid-state system.