Anharmonic Lattice Dynamics from Vibrational Dynamical Mean-Field Theory

TL;DR

This paper introduces vibrational dynamical mean-field theory (VDMFT) for modeling anharmonic lattice dynamics in solids, offering a nonperturbative, systematically improvable approach that captures quantum effects and nonlocal interactions.

Contribution

The paper develops VDMFT, a novel nonperturbative method for anharmonic lattice dynamics, combining impurity models with self-consistent baths, and demonstrates its effectiveness for optical and acoustic phonons.

Findings

Classical VDMFT agrees well with molecular dynamics for phonon properties.

Quantum VDMFT captures nuclear quantum effects at low temperatures.

Combining VDMFT with SCPH enhances nonlocal anharmonicity modeling.

Abstract

We present a vibrational dynamical mean-field theory (VDMFT) of the dynamics of atoms in solids with anharmonic interactions. Like other flavors of DMFT, VDMFT maps the dynamics of a periodic anharmonic lattice of atoms onto those of a self-consistently defined impurity problem with local anharmonicity and coupling to a bath of harmonic oscillators. VDMFT is exact in the harmonic and molecular limits, nonperturbative, systematically improvable through its cluster extensions, usable with classical or quantum impurity solvers (depending on the importance of nuclear quantum effects), and can be combined with existing low-level diagrammatic theories of anharmonicity. When tested on models of anharmonic optical and acoustic phonons, we find that classical VDMFT gives good agreement with classical molecular dynamics, including the temperature dependence of phonon frequencies and lifetimes. Using a quantum impurity solver, signatures of nuclear quantum effects are observed at low temperatures. We test the description of nonlocal anharmonicity via cellular VDMFT and the combination with self-consistent phonon (SCPH) theory, yielding the powerful SCPH+VDMFT approach.