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

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.

15 pages, 7 figures

References in corpus (8)

• Electron transport through double quantum dots
• Two-dimensional Hubbard-Holstein bipolaron
• Orbital ordering in frustrated Jahn-Teller systems
• Strong-Coupling Expansion for the Hubbard Model
• Numerical study of the $E\otimes e$ Jahn-Teller polaron and bipolaron
• Two-component Bose gas in an optical lattice at single-particle filling
• Time evolution of the Rabi Hamiltonian from the unexcited vacuum
• Interplay between Spin and Phonon Fluctuations in the double-exchange model for the manganites

Cited by in corpus (5)

• Effects of symmetry breaking in finite quantum systems
• Dynamics of finite Fermi-Hubbard and Bose-Hubbard systems
• Short note on the Rabi model
• Quantum phase crossover and chaos in generalized Jahn-Teller lattice model
• Jahn-Teller systems at half filling: crossover from Heisenberg to Ising behavior