Screening in the finite-temperature reduced Hartree-Fock model

TL;DR

This paper proves the existence of solutions in the finite-temperature reduced Hartree-Fock model for crystals with defects, demonstrating charge screening and convergence of iterative methods, with a focus on the dielectric operator.

Contribution

It establishes the existence of solutions and charge screening in the finite-temperature reduced Hartree-Fock model, and analyzes the dielectric operator's properties.

Findings

Total screening of defect charge by electrons

Convergence of self-consistent field iteration with Kerker preconditioning

Properties of the dielectric operator

Abstract

We prove the existence of solutions of the reduced Hartree-Fock equations at finite temperature for a periodic crystal with a small defect, and show total screening of the defect charge by the electrons. We also show the convergence of the damped self-consistent field iteration using Kerker preconditioning to remove charge sloshing. As a crucial step of the proof, we define and study the properties of the dielectric operator.