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arXiv · 2405.01386

The Correlation Energy of the Electron Gas in the Mean-Field Regime

Martin Ravn Christiansen·Christian Hainzl·Phan Thành Nam
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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 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.

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Martin Ravn Christiansen, Christian Hainzl, Phan Thành Nam. 2024-05-02. The Correlation Energy of the Electron Gas in the Mean-Field Regime. https://arxiv.org/abs/2405.01386

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