We prove a rigorous lower bound on the correlation energy of interacting fermions in the mean-field regime for a wide class of singular interactions, including the Coulomb potential. Combined with the upper bound obtained in {ChrHaiNam-23b}, our result establishes an analogue of the Gell-Mann--Brueckner formula c₁ρlog(ρ)+c₂ρ for the correlation energy of the electron gas in the high-density limit. Moreover, our analysis allows us to go beyond mean-field scaling while still covering the same class of potentials.
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Christiansen et al. (2024) studied this question.
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