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\(1/(N - 1)\) Expansion for an SU(N) Impurity Anderson Model: A New Large-N Scheme Based on a Perturbation Theory in U

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Low-Dimensional Functional Materials

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Abstract

Low-energy properties of an SU(N) Anderson model are studied, using the \(1/(N - 1)\) expansion based on a perturbation theory in the Coulomb interaction U. This approach is different from conventional large N theories, such as from the usual 1 ∕ N expansion and the non-crossing approximation based on the expansion in the hybridization matrix element between the impurity orbital and conduction band. In our approach the scaling factor N − 1 appears as the total number of interacting orbitals excluding the one prohibited by the Pauli principle, and it captures the low-energy local Fermi-liquid behavior correctly. We find that the next-leading-order results of the renormalized parameters agree closely with the numerical renormalization group results in a wide range of electron fillings at N = 4, where the degeneracy is still not so large. This ensures the reliability of the next-leading order results for N > 4. Furthermore, we apply this approach to nonequilibrium current through a quantum dot in the Kondo regime.

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Acknowledgements

The authors thank T. Kato and A.C. Hewson for discussions. This work is supported by the JSPS Grant-in-Aid for Scientific Research C (No. 23540375, and No. 24540316). Numerical computation was partly carried out at the Yukawa Institute Computer Facility.

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Authors and Affiliations

  1. Department of Physics, Osaka City University, Sumiyoshi-ku, Osaka, Japan

    Akira Oguri

  2. Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba, Japan

    Rui Sakano & Tatsuya Fujii

Authors
  1. Akira Oguri
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  2. Rui Sakano
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  3. Tatsuya Fujii
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Corresponding author

Correspondence to Akira Oguri .

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Editors and Affiliations

  1. , Institut für Theoretische Physik IV, Heinrich-Heine-Universität, Universitätsstrasse 1, Düsseldorf, 40225, Germany

    Reinhold Egger

  2. Laboratory for Advanced Studies, Department of Energy, Turin Polytechnic University in Tashkent, Niyazov St. 17, Tashkent, 100174, Uzbekistan

    Davron Matrasulov

  3. , Department of Physics, National University of Uzbekistan, Niyazov St. 17, Tashkent, 100174, Uzbekistan

    Khamdam Rakhimov

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Oguri, A., Sakano, R., Fujii, T. (2013). \(1/(N - 1)\) Expansion for an SU(N) Impurity Anderson Model: A New Large-N Scheme Based on a Perturbation Theory in U . In: Egger, R., Matrasulov, D., Rakhimov, K. (eds) Low-Dimensional Functional Materials. NATO Science for Peace and Security Series B: Physics and Biophysics. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6618-1_14

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