Single Impurity Anderson Model with Coulomb Repulsion between Conduction   Electrons on the Nearest-Neighbour Ligand Orbital
  We study how the Kondo effect is affected by the Coulomb interaction between conduction electrons on the basis of a simplified model. The single impurity Anderson model is extended to include the Coulomb interaction on the nearest-neighbour ligand orbital. The excitation spectra are calculated using the numerical renormalization group method. The effective bandwidth on the ligand orbital, $D^{eff}$, is defined to classify the state. This quantity decreases as the Coulomb interaction increases. In the $D^{eff} > \Delta$ region, the low energy properties are described by the Kondo state, where $\Delta$ is the hybridization width. As $D^{eff}$ decreases in this region, the Kondo temperature $T_{K}$ is enhanced, and its magnitude becomes comparable to $\Delta$ for $D^{eff} \sim \Delta$. In the $D^{eff} < \Delta$ region, the local singlet state between the electrons on the $f$ and ligand orbitals is formed. 
Ryu Takayama and Osamu Sakai