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Lower Bound on the Hartree-Fock Energy of the Electron Gas

Gontier, David; Hainzl, Christian; Lewin, Mathieu (2019), Lower Bound on the Hartree-Fock Energy of the Electron Gas, Physical Review. A, Atomic, Molecular and Optical Physics, 99, 5. 10.1103/PhysRevA.99.052501

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155109180964793.pdf (195.2Kb)
Type
Article accepté pour publication ou publié
Date
2019-05
Journal name
Physical Review. A, Atomic, Molecular and Optical Physics
Volume
99
Number
5
Publisher
American Physical Society
Publication identifier
10.1103/PhysRevA.99.052501
Metadata
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Author(s)
Gontier, David cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Hainzl, Christian
Mathematisches Institut [Tübingen]
Lewin, Mathieu cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
The Hartree-Fock ground state of a homogeneous electron gas is never translation invariant, even at high densities. As proved by Overhauser, the (paramagnetic) free Fermi gas is always unstable under the formation of spin- or charge-density waves. We give here an explicit bound on the energy gain due to the breaking of translational symmetry. Our bound is exponentially small at high density, which justifies a posteriori the use of the noninteracting Fermi gas as a reference state in the large-density expansion of the correlation energy of the homogeneous electron gas. We are also able to discuss the positive temperature phase diagram and prove that the Overhauser instability only occurs at temperatures which are exponentially small at high density. Our work sheds a new light on the Hartree-Fock phase diagram of the homogeneous electron gas.
Subjects / Keywords
Hartree-Fock ground state; Electron Gas; Density functional theory; Electron-correlation calculations; First-principles calculations; Hartree-Fock methods

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