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We study ground state properties and excitation spectra for hard-core Bosonson square and triangular lattices, at half filling, using series expansionmethods. Nearest-neighbor repulsion between the Bosons leads to the developmentof short-range density order at the antiferromagnetic wavevector, andsimultaneously a roton minima in the density excitation spectra. On thesquare-lattice, the model maps on to the well studied XXZ model, and the rotongap collapses to zero precisely at the Heisenberg symmetry point, leading tothe well known spectra for the Heisenberg antiferromagnet. On thetriangular-lattice, the collapse of the roton gap signals the onset of thesupersolid phase. Our results suggest that the transition from the superfluidto the supersolid phase maybe weakly first order. We also find several featuresin the density of states, including two-peaks and a sharp discontinuity, whichmaybe observable in experimental realization of such systems.

Collective excitations of hard-core Bosons at half filling on square and triangular lattices: Development of roton minima and collapse of roton gap