Polaron action for multimode dispersive phonon systems

TL;DR

This paper extends the path-integral approach to the polaron problem to systems with multiple dispersive phonon modes, providing a formalism for analyzing polaron properties in complex lattice systems.

Contribution

It develops an analytical formalism for the polaron action in multimode dispersive phonon systems, enabling numerical Monte Carlo studies.

Findings

Derived the polaron action for multiple phonon modes.

Provided boundary conditions for thermodynamics and spectral analysis.

Established a basis for numerical path-integral Monte Carlo methods.

Abstract

Path-integral approach to the tight-binding polaron is extended to multiple optical phonon modes of arbitrary dispersion and polarization. The non-linear lattice effects are neglected. Only one electron band is considered. The electron-phonon interaction is of the density-displacement type, but can be of arbitrary spatial range and shape. Feynman's analytical integration of ion trajectories is performed by transforming the electron-ion forces to the basis in which the phonon dynamical matrix is diagonal. The resulting polaron action is derived for the periodic and shifted boundary conditions in imaginary time. The former can be used for calculating polaron thermodynamics while the latter for the polaron mass and spectrum. The developed formalism is the analytical basis for numerical analysis of such models by path-integral Monte Carlo methods.