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A holographic model of the Kondo effect

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Abstract

We propose a model of the Kondo effect based on the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence, also known as holography. The Kondo effect is the screening of a magnetic impurity coupled anti-ferromagnetically to a bath of conduction electrons at low temperatures. In a (1+1)-dimensional CFT description, the Kondo effect is a renormalization group flow triggered by a marginally relevant (0+1)-dimensional operator between two fixed points with the same Kac-Moody current algebra. In the large-N limit, with spin SU(N) and charge U(1) symmetries, the Kondo effect appears as a (0+1)-dimensional second-order mean-field transition in which the U(1) charge symmetry is spontaneously broken. Our holographic model, which combines the CFT and large-N descriptions, is a Chern-Simons gauge field in (2+1)-dimensional AdS space, AdS 3, dual to the Kac-Moody current, coupled to a holographic superconductor along an AdS 2 sub-space. Our model exhibits several characteristic features of the Kondo effect, including a dynamically generated scale, a resistivity with power-law behavior in temperature at low temperatures, and a spectral flow producing a phase shift. Our holographic Kondo model may be useful for studying many open problems involving impurities, including for example the Kondo lattice problem.

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Authors and Affiliations

  1. Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), Föhringer Ring 6, 80805, München, Germany

    Johanna Erdmenger

  2. Raymond and Beverly Sackler School of Physics and Astronomy, Tel-Aviv University, Ramat-Aviv, 69978, Israel

    Carlos Hoyos

  3. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, CB3 0WA, United Kingdom

    Andy O’Bannon

  4. Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford, OX1 3NP, United Kingdom

    Andy O’Bannon

  5. National Center for Theoretical Sciences, Physics Division, No. 101, section 2, Kuang Fu Road, Hsinchu, Taiwan, 300, China

    Jackson Wu

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  1. Johanna Erdmenger
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Correspondence to Andy O’Bannon.

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ArXiv ePrint: 1310.3271

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Erdmenger, J., Hoyos, C., O’Bannon, A. et al. A holographic model of the Kondo effect. J. High Energ. Phys. 2013, 86 (2013). https://doi.org/10.1007/JHEP12(2013)086

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