We study Kondo dynamics in the single-impurity Anderson model in terms of operator basis vectors. A complete set of basis vectors is determined by using the Hamiltonian of this model. Then, we construct a reduced Liouville space by eliminating some basis vectors that are unimportant in the Kondo regime, and we obtain the retarded Green's function. We compare our results with those of Fermi liquid theory and the numerical renormalization group method.

Journal of Physics Condensed MatterMay 17, 20117 citations

Fermi-liquid theory for the single-impurity Anderson model

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arXiv:1108.5121

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

K. Kikoin

Published Aug 25, 2011• 0 citations

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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.

DOI: 10.48550/arxiv.1108.5121

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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

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.

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

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.

{T}^{2}, {V}^{2}

, and

{B}^{2}

are found to change sign during the Kondo to empty-orbital crossover. The crossover becomes universal in the limit that the local interaction is much larger than the level width. For completeness, we also compute the shot noise and discuss the resulting Fano factor.