Properties of periodic Dirac-Fock functional and minimizers - Université Paris Dauphine
Pré-Publication, Document De Travail Année : 2024

Properties of periodic Dirac-Fock functional and minimizers

Résumé

Existence of minimizers for the Dirac-Fock model for crystals was recently proved by Paturel and Séré and the authors [9]. In this paper, inspired by Ghimenti and Lewin's result [12] for the periodic Hartree-Fock model, we prove that the Fermi level of any periodic Dirac-Fock minimizer is either empty or totally filled when α/c\leq C_{cri} and α > 0. Here c is the speed of light, α is the fine structure constant, and C cri is a constant only depending on the number of electrons and on the charge of nuclei per cell. More importantly, we provide an explicit upper bound for C_{cri} .

Our result implies that any minimizer of the periodic Dirac-Fock model is a projector when α/c\leq C_{cri} and α > 0 In particular, the non-relativistic regime (i.e., c >>1) and the weak coupling regime (i.e., 0< α <<1) are covered.

The proof is based on a delicate study of a second-order expansion of the periodic Dirac-Fock functional composed with a retraction that was introduced by Séré in [23] for atoms and molecules and later extended to the case of crystals in [9].

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Dates et versions

hal-04700602 , version 1 (17-09-2024)

Identifiants

  • HAL Id : hal-04700602 , version 1

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Isabelle Catto, Long Meng. Properties of periodic Dirac-Fock functional and minimizers. 2024. ⟨hal-04700602⟩
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