Single Impurity Anderson Model with Coulomb Repulsion between Conduction Electrons on the Nearest-Neighbour Ligand Orbital

TL;DR

This paper investigates how Coulomb interactions on ligand orbitals influence the Kondo effect in the single impurity Anderson model, revealing a transition from Kondo to local singlet states as effective bandwidth decreases.

Contribution

The study extends the Anderson model to include Coulomb interactions on ligand orbitals and analyzes the resulting effects using numerical renormalization group methods.

Findings

Effective bandwidth decreases with Coulomb interaction.

Kondo temperature is enhanced when effective bandwidth exceeds hybridization width.

Transition from Kondo state to local singlet state occurs as effective bandwidth drops below hybridization width.

Abstract

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.