Variational ground state for the periodic Anderson model with an indirect hybridization

Abstract

As the direct on-site hybridization is forbidden by inversion symmetry in most of the mixed-valence compounds, an indirect on-site hybridization mediated by phonons has been introduced into the periodic Anderson model to constitute our model system. Then we try to construct a variational ground state for the model Hamiltonian by the following steps. First, we develop a new procedure to transform the model Hamiltonian by a unitary transformation of the displacement-operator type. Second, a two-phonon coherent state is taken as the trial-state vector for the ground state of the phonon subsystem and the parameters of the two-phonon coherent state, which are regarded as the adjustable parameters of the variational treatment, remain to be determined. Third, a Bogoliubov transformation is introduced to deal with the electron subsystem; the ground state and low-lying excited states are constructed directly. Finally, the parameters of the two-phonon coherent state are adjusted to ensure that the energy functional of our variational ground state is a stable minimum. Numerical calculations have been done and a nonzero energy gap and fluctuating valence have been obtained in various cases. Our results could be used to explain the small energy gap and valence-fluctuation phenomena observed in some Sm-based compounds.