Gell-Mann matrices for Kondo and mixed-valence effects

The concept of dynamical symmetries is applied to the Anderson model with repulsive and attractive interaction U in the Kondo and mixed valence regimes. 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 4-th rank, which form the set of group generators describing the excitation spectra in the charge and spin sectors. The multistage Kondo screening is also interpreted as a manifestation 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.