The excitation spectrum of Bose gases interacting through singular potentials

We consider systems of N bosons in a box of volume one, interacting through a repulsive two-body potential of the form κ N^{3β} V(N^β x) . For all β in (0;1), and for sufficiently small positive coupling constant, we establish the validity of Bogolyubov theory, identifying the ground state energy and the low-lying excitation spectrum up to errors that vanish in the limit of large N.