Finite E x beta Jahn-Teller Systems: A Continued-Fraction Approach

TL;DR

This paper introduces a recursive continued-fraction method to analyze electron-phonon interactions in small Jahn-Teller systems, revealing how spectra are affected by phonon coupling and system size.

Contribution

A novel recursive approach using continued fractions for calculating Green's functions in small $E\otimes\beta$ Jahn-Teller systems, including models with one and two electrons.

Findings

Spectra are significantly altered by single phonon coupling.

Spectral features are robust against increasing phonon number.

Method effectively models electron-phonon interactions in small systems.

Abstract

A recursive method is developed to treat electrons coupled to phonons. It is applied to small systems with $E\otimes\beta$ Jahn-Teller coupling. Two cases are considered, a model with one electron and two orbitals on a single site (related to the Rabi Hamiltonian) and a model with two electrons on two sites. The corresponding Green's functions are represented by rational functions. It is found that the spectra change substantially when one phonon couples to the electron but are relatively robust under an increasing number of phonons.