Simple spinless mixed-valence model. I. Coherent-hybridization states versus virtual-bound states

We consider a model consisting of spinless localized $4f$ levels interacting with spinless extended $5d$ states via a hybridization V and a local Coulomb repulsion Ufd. Using the renormalization-group technique we derive the scaling laws of the system within the leading and next-leading logarithmic approximation. We obtain that if UfdV the mixed-valence states are extended and coherent, while if UfdV the valence fluctuations are mainly local and incoherent.