The Gell-Mann–Brueckner Formula for the Correlation Energy of the Electron Gas: A Rigorous Upper Bound in the Mean-Field Regime

We prove a rigorous upper bound on the correlation energy of interacting fermions in the mean-field regime for a wide class of interaction potentials. Our result covers the Coulomb potential, and in this case we obtain the analogue of the Gell-Mann–Brueckner formula c 1 ρ log ρ + c 2 ρ in the high d...

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Bibliographic Details
Published inCommunications in mathematical physics Vol. 401; no. 2; pp. 1469 - 1529
Main Authors Christiansen, Martin Ravn, Hainzl, Christian, Nam, Phan Thành
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2023
Springer Nature B.V
Subjects
Classical and Quantum Gravitation
Complex Systems
Coulomb potential
Electron gas
Fermions
Mathematical and Computational Physics
Mathematical Physics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
Upper bounds
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Summary:We prove a rigorous upper bound on the correlation energy of interacting fermions in the mean-field regime for a wide class of interaction potentials. Our result covers the Coulomb potential, and in this case we obtain the analogue of the Gell-Mann–Brueckner formula c 1 ρ log ρ + c 2 ρ in the high density limit. We do this by refining the analysis of our bosonization method to deal with singular potentials, and to capture the exchange contribution which is absent in the purely bosonic picture.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-023-04672-2