Abstract
We study the ground state of hard-core bosons with nearest-neighbor hopping and nearest-neighbor interactions on the triangular and Kagom\'e lattices by mapping to a system of spins ($S={1\over2}$), which we analyze using spin-wave theory. We find that the both lattices display superfluid and supersolid (a coexistence of superfluid and solid) order as the parameters and filling are varied. Quantum fluctuations seem large enough in the Kagom\'e system to raise the interesting possibility of a disordered ground state.
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