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 \cite{ ChrHaiNam-23b}, our result establishes an analogue of the Gell-Mann--Brueckner formula $c_{ 1}\rho\log\left(\rho\right)+c_{ 2}\rho$ 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.
Categories: math-ph math.MP