Decay of Interatomic Force Constants in the Reduced Hartree-Fock Model

TL;DR

This paper analyzes how interatomic force constants decay in perfect crystals within the reduced Hartree-Fock model, showing exponential decay at finite temperature and algebraic decay in insulators at zero temperature.

Contribution

It provides a detailed theoretical analysis of the decay rates of interatomic force constants in different electronic states within the reduced Hartree-Fock framework.

Findings

Force constants decay exponentially at finite temperature.

In insulators, decay follows an algebraic dipole-dipole interaction pattern.

The decay behavior depends on electronic temperature and material properties.

Abstract

We study the decay of the interatomic force constants (equivalently, the smoothness properties of the dynamical matrix) in perfect crystals both at finite electronic temperature, and for insulators at zero temperature, within the reduced Hartree-Fock approximation (also called Random Phase Approximation). At finite temperature the electrons are mobile, leading to exponential decay of the force constants. In insulators, there is incomplete screening, leading to an algebraic decay of dipole-dipole interaction type.