Path Integral Computation of Phonon Anharmonicity

TL;DR

This paper introduces a path integral approach to compute the partition function of an oscillator with electron-phonon interactions, revealing how anharmonicities affect phonon heat capacity and depend on coupling strength.

Contribution

It develops a novel path integral method to evaluate anharmonic effects in phonons at any temperature, specifically applied to the Su-Schrieffer-Heeger model.

Findings

Phonon heat capacity peaks shift with electron-phonon coupling strength.

High energy oscillators are less affected by anharmonicities.

The method allows for detailed temperature-dependent analysis of anharmonic effects.

Abstract

The partition function of an oscillator disturbed by a set of electron particle paths has been computed by a path integral method which permits to evaluate at any temperature the relevant cumulant terms in the series expansion. The time dependent source current peculiar of the semiclassical Su-Schrieffer-Heeger model induces large electron-phonon anharmonicities on the phonon subsystem. As a main signature of anharmonicity the phonon heat capacity shows a peak whose temperature location strongly varies with the strength of the {\it e-ph} coupling. High energy oscillators are less sensitive to anharmonic perturbations.