Two-dimensional Bose-Hubbard model for helium on graphene
Jiangyong Yu, Ethan Lauricella, Mohamed M. Elsayed, Kenneth Shepherd, Nathan Nichols, Todd Lombardi, Sang Wook Kim, Carlos Wexler, Juan M. Vanegas, Taras I. Lakoba, Valeri N. Kotov, Adrian Del Maestro
Abstract
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 $(U\ensuremath{\approx}\ensuremath{\infty})$, repulsive nearest-neighbor $(V>0)$ and small attractive $({V}^{\ensuremath{'}}<0)$ 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 $^{4}\mathrm{He}$ 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.