Excitation spectra of hard-core bosons on square and triangular lattices in superfluid phase

Excitation spectra of hard-core bosons with nearest-and next-nearest-neighbor interactions on square and triangular lattices in the superfluid phase are studied using the spin-wave theory. We go beyond the standard linear spin-wave approximation calculating corrections due to spin-wave interaction. Account for the spin-wave interaction considerably improves the quantitative description of the excitation spectra. The behavior of the spectra is analyzed in detail at different particle densities and relations between the interaction parameters. Particular attention is given to the spectrum minima with the aim to find out the conditions for instability of the superfluid phase. We show that for a triangular lattice at high enough next-nearest-neighbor repulsion there appears a true roton minimum inside the Brillouin zone located on the line connecting the zone center with the midpoint of the face of the zone boundary. The obtained analytical results are in excellent quantitative agreement with the numerical simulations known from literature.