Third Order Corrections to the Ground State Energy of a Bose Gas in the Gross-Pitaevskii Regime

For a translation invariant system of N bosons in the Gross–Pitaevskii regime, we establish a precise bound for the ground state energy EN. While the leading, order N, contribution to EN has been known since (Lieb et al. in Phys Rev A 61:043602, 2000; Lieb and Yngvason in Phys Rev Lett 80:2504–2507, 1998) and the second order corrections (of order one) have been first determined in Boccato et al. (Acta Math 222(2):219–335, 2019), our estimate also resolves the next term in the asymptotic expansion of EN, which is of the order (logN)/N.