Abstract
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- 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 , where is the degeneracy of the rare-earth ion, allowing a self-consistent calculation of the -electron spectral function to order that is valid in both the mixed-valence and Kondo regimes. The extension to the lattice is outlined and some preliminary results reported.
- Received 29 August 1983
DOI:https://doi.org/10.1103/PhysRevB.29.3035
©1984 American Physical Society