The GellMannBrueckner Formula for the Correlation Energy of the Electron Gas: A Rigorous Upper Bound in the MeanField Regime
Abstract
We prove a rigorous upper bound on the correlation energy of interacting fermions in the meanfield regime for a wide class of interaction potentials. Our result covers the Coulomb potential, and in this case we obtain the analogue of the GellMannBrueckner formula c_{1}ρ log(ρ )+c_{2}ρ in the high density limit. We do this by refining the analysis of our bosonization method to deal with singular potentials, and to capture the exchange contribution which is absent in the purely bosonic picture.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 July 2023
 DOI:
 10.1007/s00220023046722
 arXiv:
 arXiv:2208.01581
 Bibcode:
 2023CMaPh.401.1469C
 Keywords:

 Mathematical Physics
 EPrint:
 50 pages, final version