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...
Saved in:
Published in | Communications in mathematical physics Vol. 401; no. 2; pp. 1469 - 1529 |
---|---|
Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.07.2023
Springer Nature B.V |
Subjects | |
Online Access | Get full text |
Cover
Loading…
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 |