Phonon Thermodynamics versus Electron-Phonon Models

TL;DR

This study uses path integral formalism to analyze phonon thermodynamics in Holstein and Su-Schrieffer-Heeger models, revealing significant electron-phonon anharmonic effects in the latter, especially in heat capacity behavior.

Contribution

It introduces a method to compute anharmonic cumulant series in e-ph models and compares thermodynamic effects between two prominent models.

Findings

No anharmonic effects in Holstein model's free energy derivatives.

Large anharmonicities detected in SSH model, affecting heat capacity.

Temperature-dependent phonon heat capacity peak observed in SSH model.

Abstract

Applying the path integral formalism we study the equilibrium thermodynamics of the phonon field both in the Holstein and in the Su-Schrieffer-Heeger models. The anharmonic cumulant series, dependent on the peculiar source currents of the {\it e-ph} models, have been computed versus temperature in the case of a low energy oscillator. The cutoff in the series expansion has been determined, in the low $T$ limit, using the constraint of the third law of thermodynamics. In the Holstein model, the free energy derivatives do not show any contribution ascribable to {\it e-ph} anharmonic effect. We find signatures of large {\it e-ph} anharmonicities in the Su-Schrieffer-Heeger model mainly visible in the temperature dependent peak displayed by the phonon heat capacity.