Jahn-Teller effect in the augmented Hubbard model

We investigate the effects induced by the interplay of microscopic degrees of freedom. In many cases, one has to consider spin and orbital degeneracy to explain complex structures of magnetic and orbital order. Frequently, attention is focused on electronic correlations. We study how the interaction of electrons with lattice degrees of freedom modifies the pure electronic case. Because of orbital degeneracy we have to deal with the Jahn-Teller effect. In particular, the E Jahn-Teller effect allows a perturbative approach. Assuming that the excitation energies dominate the hopping rate, we derive an effective model and analyze the interaction-induced symmetry breaking. The additional orbital degree of freedom results in a spin-orbital model and phonons are taken into account as modified coupling parameters. A quantum mechanical treatment of phonons results in an exponentially quenched orbital exchange coupling. Furthermore, by considering electronic symmetry one obtains symmetry breaking in the orbital sector. This was also found when Hund’s rule coupling was taken into account, but in this case higher symmetry can be restored by proper choice of parameters, which is not the case for Jahn-Teller coupling. Surprisingly, adiabatic treatment shows neither exponential damping nor nonrestorable symmetry breaking in the orbital sector.