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Spin symmetry breaking in the translation-invariant Hartree-Fock Uniform Electron Gas

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1812.07679.pdf (534.6Kb)
Date
2019
Dewey
Sciences connexes (physique, astrophysique)
Sujet
phase diagram; electron gas; Hartree--Fock
Journal issue
Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal
Volume
21
Number
4
Publication date
2019
Article pages
3388–3423
Publisher
SIAM - Society for Industrial and Applied Mathematics
DOI
http://dx.doi.org/10.1137/19M1243142
URI
https://basepub.dauphine.fr/handle/123456789/19623
Collections
  • CEREMADE : Publications
Metadata
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Author
Gontier, David
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Lewin, Mathieu
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Type
Article accepté pour publication ou publié
Abstract (EN)
We study the breaking of spin symmetry for the nonlinear Hartree--Fock model describing an infinite translation-invariant interacting quantum gas (fluid phase). At zero temperature and for the Coulomb interaction in three space dimensions, we can prove the existence of a unique first order transition between a pure ferromagnetic phase at low density and a paramagnetic phase at high density. Multiple first or second order transitions can happen for other interaction potentials, as we illustrate on some examples. At positive temperature $T>0$ we compute numerically the phase diagram in the Coulomb case. We find the paramagnetic phase at high temperature or high density and a region where the system is ferromagnetic. We prove that the equilibrium state is unique and paramagnetic at high temperature or high density.Read More: https://epubs.siam.org/doi/abs/10.1137/19M1243142

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