Multistage Kondo effect as a manifestation of dynamical symmetries in the single- and two-electron tunneling

TL;DR

This paper explores the multistage Kondo effect through the lens of dynamical symmetries, revealing an underlying SU(4) symmetry in the Anderson model that governs charge and spin excitations.

Contribution

It introduces a formulation of the Kondo effect using dynamical SU(4) symmetry, unifying spin and charge excitations in the Anderson model with both repulsive and attractive interactions.

Findings

Multistage Kondo screening described by SU(4) symmetry.

SU(4) symmetry explains similarities between positive and negative U models.

Reformulation of Anderson Hamiltonian using Gell-Mann matrices.

Abstract

The concept of dynamical symmetries is used for formulation of the renormalization group approach to the Kondo effect in the Anderson model with repulsive and attractive interaction $U$. It is shown that the generic local symmetry of the Anderson Hamiltonian is determined by the SU(4) Lie group. The Anderson Hamiltonian is rewritten in terms of the Gell-Mann matrices of the 4-th rank, which form the set of group generators and the basis for construction of irreducible vector operators describing the excitation spectra in the charge and spin sectors. The multistage Kondo sceening is described in terms of the local SU(4) dynamical symmetry. It is shown that the similarity between the conventional Kondo cotunneling effect for spin 1/2 in the positive $U$ model and the Kondo resonance for pair tunneling in the negative $U$ model is a direct manifestation of implicit SU(4) symmetry of the Anderson/Kondo model.