Hainzl, Christian; Porta, Marcello; Rexze, Felix
(2020):
On the Correlation Energy of Interacting Fermionic Systems in the MeanField Regime.
In: Communications in Mathematical Physics, Vol. 374, No. 2: pp. 485524

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Abstract
We consider a system of N>>interacting fermionic particles in three dimensions, confined in a periodic box of volume 1, in the meanfield scaling. We assume that the interaction potential is bounded and small enough. We prove upper and lower bounds for the correlation energy, which are optimal in their Ndependence. Moreover, we compute the correlation energy at leading order in the interaction potential, recovering the prediction of second order perturbation theory. The proof is based on the combination of methods recently introduced for the study of fermionic manybody quantum dynamics together with a rigorous version of secondorder perturbation theory, developed in the context of nonrelativistic QED.