We consider a Bose gas on the 3d unit torus in the Gross-Pitaevskii regime and compute the ground state energy up to an error which for large N vanishes faster than N^{−1} log N. Our result is compatible with a prediction formulated by theoretical physicists in the 50’s for the correction beyond the Lee-Huang-Yang formula in the thermodynamic limit.
The proof involves a renormalization of the Hamiltonian through conjugation with unitary operators that implement two-body and three-body correlations. We need in particular a non-trivial improvement of the structure of three-body correlations
compared to earlier results.
Joint work with Cristina Caraci (University of Geneva), Diane Saint Aubin (University of Zurich), and Benjamin Schlein (University of Zurich).