  Quantum Monte Carlo (QMC) simulation has uncovered nonzero Berry curvature
and bosonic edge states in hardcore-Bose-Hubbard model on the gapped honeycomb
lattice. The competition between the chemical potential and staggered onsite
potential leads to an interesting quantum phase diagram comprising superfluid
phase, Mott insulator, and charge density wave insulator. In this paper, we
present a semiclassical perspective of this system by mapping to a spin-$1/2$
quantum XY model. We give an explicit analytical origin of the quantum phase
diagram, the Berry curvatures, and the edge states using semiclassical
approximations. We find very good agreements between the semiclassical analyses
and the QMC results. Our results show that the topological properties of
hardcore-Bose-Hubbard model are the same as those of magnon in the
corresponding quantum spin system. Our results are applicable to systems of
ultracold bosonic atoms trapped in honeycomb optical lattices.
