Anharmonic phonon behavior via irreducible derivatives: self-consistent perturbation theory and molecular dynamics

TL;DR

This paper develops a self-consistent perturbation theory framework using irreducible derivatives to accurately compute anharmonic phonon interactions and linewidths in CaF2, validated against molecular dynamics simulations.

Contribution

It introduces an efficient irreducible derivative approach for self-consistent anharmonic phonon calculations applicable in quantum and classical regimes.

Findings

4-phonon sunset diagram significantly affects linewidths above 500 K

Self-consistent calculations match molecular dynamics results up to 900 K

Irreducible derivative method enhances robustness of anharmonic phonon analysis

Abstract

Cubic phonon interactions are now regularly computed from first principles, and the quartic interactions have begun to receive more attention. Given this realistic anharmonic vibrational Hamiltonian, the classical phonon Green's function can be precisely measured using molecular dynamics, which can then be used to rigorously assess the range of validity for self-consistent diagrammatic approaches in the classical limit. Here we use the bundled irreducible derivative approach to efficiently and precisely compute the cubic and quartic phonon interactions of CaF$_2$, systematically obtaining the vibrational Hamiltonian purely in terms of irreducible derivatives. non frequency shifts and linewidths, We demonstrate that the 4-phonon sunset diagram has an important contribution to the optical phonon linewidths beyond $T=500$ K. Reasonable results are obtained even at $T=900$ K when performing self-consistency using the 4-phonon loop diagram and evaluating the 3-phonon bubble and 4-phonon sunset diagrams post self-consistency. Further improvements are obtained by performing quasiparticle perturbation theory, where both the 4-phonon loop and the real part of the 3-phonon bubble are employed during self-consistency. Our irreducible derivative approach to self-consistent perturbation theory is a robust tool for studying anharmonic phonons in both the quantum and classical regimes.