The correlation energy of the electron gas in the mean-field regime
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.
Fields of Study & Subjects
Gas Dynamics and Kinetic Theory
Plasma Diagnostics and Applications
Atomic and Molecular Physics
Publication details
- Journal / source
- Journal of the American Mathematical Society
- Publisher
- American Mathematical Society (AMS)
- Volume
- 40
- Issue
- 1
- Pages
- 235–316
- Publication date
- 27 May 2026
- Language
- EN