New approach to the mixed-valence problem

A new formulation of the mixed-valence problem is presented in which the singlet valence state of a rare-earth ion is represented by a zero-energy boson and the spinning state by a spin-j fermion. This representation avoids the need to use Hubbard operators with awkward algebras and avails itself of standard techniques for dealing with interacting quantum systems. In particular, a Feynman-diagram expansion for the thermodynamic variables and spectral functions can be developed. The advantages of the approach are illustrated for the mixed-valence impurity problem. Vertex corrections are found to be O(1N²), where N is the degeneracy of the rare-earth ion, allowing a self-consistent calculation of the f-electron spectral function to order O(1N²) that is valid in both the mixed-valence and Kondo regimes. The extension to the lattice is outlined and some preliminary results reported.