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

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.