The reduced Hartree-Fock model for short-range quantum crystals with defects

Abstract

In this article, we consider quantum crystals with defects in the reduced Hartree-Fock framework. The nuclei are supposed to be classical particles arranged around a reference periodic configuration. The perturbation is assumed to be small in amplitude, but need not be localized in a specific region of space or have any spatial invariance. Assuming Yukawa interactions, we prove the existence of an electronic ground state, solution of the self-consistent field equation. Next, by studying precisely the decay properties of this solution for local defects, we are able to expand the density of states of the nonlinear Hamiltonian of a system with a random perturbation of Anderson-Bernoulli type, in the limit of low concentration of defects. One important step in the proof of our results is the analysis of the dielectric response of the crystal to an effective charge perturbation.

References in corpus (1)

• A new approach to the modelling of local defects in crystals: the reduced Hartree-Fock case

Cited by in corpus (4)

• QM/MM methods for crystalline defects. Part 1: Locality of the tight binding model
• Mean--field stability for the junction of quasi 1D systems with Coulomb interactions
• Convergence Rates from Yukawa to Coulomb Interaction in the Thomas-Fermi-von Weizsäcker Model
• The reduced Hartree-Fock model with self-generated magnetic fields