Year: 2026
Type: article
Abstract: 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 by Christiansen, Hainzl, and Nam [Comm. Math. Phys. 401 (2023), pp. 1469–1529], our result establishes an analogue of the Gell-Mann–Brueckner formula c 1 ρ log ( ρ ) + c 2 ρ 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.
DOI: 10.1090/jams/1080
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4396648988