The Excitation Spectrum of Two-Dimensional Bose Gases in the Gross-Pitaevskii Regime

We consider a system of N bosons, in the two-dimensional unit torus. We assume particles to interact through a repulsive two body potential, with a scattering length that is exponentially small in N (Gross-Pitaevskii regime). In this setting, we establish the validity of the predictions of Bogoliubov theory, determining the ground state energy of the Hamilton operator and its low-energy excitation spectrum, up to errors that vanish in the limit N ? 8.