Hard-Core Bosons on a Two-Dimensional Square Optical Super lattice

In this work, we theoretically study hard-core bosons on a two-dimensional square optical superlattice at T = 0. First of all, we present the mean field phase diagram of this model in terms of the chemical potential i and the alternating potential strength A. Besides a superfluid (SF) phase at Delta = 0 and a charge density wave (CDW) phase in the large A at half filling, we demonstrate that a supersolid (SS) phase emerges in the moderate A. Then, we focus on the mu= 0, e.g., half filling case, using large-S semi-classical spin-wave approximation to study the SS to CDW quantum phase transition. In particular, we calculate the ground-state energy and the superfluid density at the level of 1/S correction. We then compare the spin-wave results with the large scale quantum Monte Carlo (QMC) simulations using the cluster stochastic series expansion (CSSE) algorithm, and find that while the spin wave method is intuitive with clear physical pictures, the quantum critical point is quite different from that of numerical results which is believed to be accurate. We suggest that as simple as it is, this model still exhibits strong quantum fluctuations near the quantum critical point beyond the power of semiclassical spin-wave approach.