Local polaron model in a fluctuating-valence system.

Abstract

The local polaron problem---in which a local f-electron level, hybridized with conduction electrons in a wide band, is coupled to a local phonon mode---is solved by a variational approach. The nonadiabatic effects due to finite phonon frequency \ensuremath{\omega} are treated through a variational polaron wave function, in which the softening of the phonon frequency as a result of electron-phonon interaction is taken into consideration by means of the squeezing transformation. We have found that the quantum fluctuations of the phonon mode gradually smooth out the abrupt transition of the f-level occupancy when the effective f level increases across the Fermi energy. There is a critical value of \ensuremath{\omega} above which the transition becomes continuous. In order to improve our treatment for the degenerate case when \ensuremath{\omega} is small, the method of the ``orthogonality catastrophe theorem'' is used, and an energy-dependent form for the local potential of conduction electrons has been introduced. Our results show that the transition of the f-level occupancy should be continuous for finite \ensuremath{\omega}, although it becomes steeper and steeper with decreasing \ensuremath{\omega}. Also, it is pointed out that because of the quantum fluctuation of the phonon mode, a significant renormalization of the virtual f-level width never occurs even if the conditions described by previous authors for its occurrence are satisfied.