Path Integral Methods in the Su-Schrieffer-Heeger Polaron Problem

TL;DR

This paper develops a path integral approach to analyze the Su-Schrieffer-Heeger polaron model in one and two dimensions, revealing glass-like low-temperature behavior and effects of anharmonic interactions.

Contribution

It introduces a novel path integral framework for the SSH model, incorporating variable-range hopping and quantum electron paths, extending analysis to higher dimensions.

Findings

Unusual upturn in heat capacity over temperature ratio at low T.

Higher dimensional lattices show more pronounced glass-like features.

Electron-phonon anharmonic effects influence phonon subsystem behavior.

Abstract

I propose a path integral description of the Su-Schrieffer-Heeger Hamiltonian, both in one and two dimensions, after mapping the real space model onto the time scale. While the lattice degrees of freedom are classical functions of time and are integrated out exactly, the electron particle paths are treated quantum mechanically. The method accounts for the variable range of the electronic hopping processes. The free energy of the system and its temperature derivatives are computed by summing at any $T$ over the ensemble of relevant particle paths which mainly contribute to the total partition function. In the low $T$ regime, the {\it heat capacity over T} ratio shows un upturn peculiar to a glass-like behavior. This feature is more sizeable in the square lattice than in the linear chain as the overall hopping potential contribution to the total action is larger in higher dimensionality. The effects of the electron-phonon anharmonic interactions on the phonon subsystem are studied by the path integral cumulant expansion method.