Superfluid to Mott-insulator transition of hardcore bosons in a superlattice

We study the superfluid to Mott-insulator (SF-MI) transition of hardcore bosons in commensurate superlattices in two and three dimensions. We focus on the special case where the superlattice has period two and the system is at half filling. We obtain exact numerical results by using the stochastic series expansion (SSE) algorithm, and compute various properties of the system, such as the ground-state energy, the fraction of bosons in the zero-momentum mode, the superfluid density, and the compressibility. With finite-size scaling, we find the critical points of the phase transition. We also explore the extent to which several approximate solutions such as mean-field theory, with and without spin-wave corrections, can help one gain analytical insight into the behavior of the system in the vicinity of the phase transition.