Properties of the periodic Hartree-Fock minimizer

TL;DR

This paper investigates the properties of minimizers in the periodic Hartree-Fock model for crystals, proving they are projectors and characterizing their Fermi levels, thus deepening understanding of electronic structure in periodic systems.

Contribution

It demonstrates that all minimizers are projectors and satisfy a specific nonlinear equation, extending atomic Hartree-Fock properties to periodic systems.

Findings

Minimizers are necessarily projectors.

Fermi level is either empty or fully filled.

Minimizers satisfy a nonlinear equation similar to atomic cases.

Abstract

We study the periodic Hartree-Fock model used for the description of electrons in a crystal. The existence of a minimizer was previously shown by Catto, Le Bris and Lions (Ann. Inst. H. Poincare Anal. Non Lineaire} 18 (2001), no.6, 687--760). We prove in this paper that any minimizer is necessarily a projector and that it solves a certain nonlinear equation, similarly to the atomic case. In particular we show that the Fermi level is either empty or totally filled.