Date of Award


Document Type


Degree Name

Master of Science (MS)



First Advisor

Valeri N. Kotov


An exciting development in the field of correlated systems is the possibilityof realizing two-dimensional (2D) phases of quantum matter. For a systems 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 ≈ ∞) and repulsive nearest-neighbor (V > 0) interactions. In this work, we focus on the calculations of single particle properties of the model such as the hopping parameter t. This is accomplished via Wannier Theory and Band structure calculations, which proves to be reliable methods of calculating such properties. For the many body properties such as V , we show that Wannier Theory breaks down and other methods are preferably used. The result places the ground state of the first layer of 4He adsorbed on graphene deep in the commensurate solid phase with 1/3 of the sites on the dual triangular lattice occupied



Number of Pages

76 p.