Simple spinless mixed-valence model. II. Solution of the isolatedf-level problem

Abstract

We consider an isolated spinless localized $4f$ level interacting with a spinless Fermi sea through a hybridization and a Coulomb repulsion. The problem is mapped onto the anisotropic Kondo problem in an external magnetic field. Using the Ward identity for the total charge conservation we derive an exact relation between the specific heat and the charge susceptibility at low temperatures. Using a renormalization-group approach and the analogy to the x-ray threshold problem, we show that the impurity behaves like a resonant level with a renormalized resonance width. We give expressions for the charge susceptibility and the specific heat. The extension to a compound of noninteracting $f$-level impurities shows that discontinuous valence transitions are possible in models involving local and incoherent valence fluctuations.