Mean-field models for disordered crystals

TL;DR

This paper develops a mathematical framework for mean-field electronic structure models of disordered crystals, proving existence and uniqueness of ground states for the reduced Hartree-Fock model with different interactions.

Contribution

It establishes the existence and uniqueness of the ground state density for disordered crystals within a rigorous mean-field model, including both Yukawa and Coulomb interactions.

Findings

Proved existence of energy minimizer per unit volume.

Established uniqueness of the ground state density.

Connected the model to the thermodynamic limit of supercell models.

Abstract

In this article, we set up a functional setting for mean-field electronic structure models of Hartree-Fock or Kohn-Sham types for disordered crystals. The electrons are quantum particles and the nuclei are classical point-like articles whose positions and charges are random. We prove the existence of a minimizer of the energy per unit volume and the uniqueness of the ground state density of such disordered crystals, for the reduced Hartree-Fock model (rHF). We consider both (short-range) Yukawa and (long-range) Coulomb interactions. In the former case, we prove in addition that the rHF ground state density matrix satisfies a self-consistent equation, and that our model for disordered crystals is the thermodynamic limit of the supercell model.