Effect of a magnetic field on an $E\otimes \epsilon$ Jahn-Teller system: Berry phase and optical properties

We have studied the effect of a uniform magnetic field on Berry phase (BP) and optical properties (absorption for right-hand and left-hand circularly polarized light) of an $E\otimes \epsilon$ Jahn-Teller (JT) system. The magnetic field is applied along the trigonal axis of a trigonal-symmetry compound. Dynamical properties are exactly determined in the framework of the Lanczos algorithm, because the coefficients of the recursion procedure can be put in analytic form. Different strength of linear electron-phonon coupling and magnetic field are studied, and the connection with BP is analyzed.