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Holographic Kondo Models

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Strongly Coupled Field Theories for Condensed Matter and Quantum Information Theory

Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 239))

Abstract

These lecture notes are devoted to studying the Kondo problem from the perspective of gauge/gravity duality. This duality is a major recent development within theoretical physics. It maps strongly coupled quantum systems to weakly coupled gravity theories and thus provides a new approach to their description. The Kondo model as originally proposed by J. Kondo in 1961 played a decisive role in the development of major concepts in quantum field theory, such as the renormalization group and the use of conformal symmetry. It describes describes a spin impurity interacting with a free electron gas: At low energies, the impurity is screened and there is a logarithmic rise of the resistivity. In quantum field theory, this amounts to a negative beta function for the impurity coupling and the theory flows to a non-trivial IR fixed point. In these lectures we construct and examine a variant of the Kondo model within gauge/gravity duality. The motivation is twofold: On the one hand, the model may be used for calculating observables for the case of a spin impurity interacting with a strongly correlated electron gas. On the other hand, the models allows for new insights into the working mechanisms of gauge/gravity duality. For constructing the gravity dual, we consider a version of the Kondo model with SU(N) spin at large N, in which the ambient electrons are strongly coupled even before the interaction with the impurity is switched on. We present the brane construction which motivates a gravity dual Kondo model and use this model to calculate the impurity entanglement entropy. The resistivity has a power-law behaviour in this model. We also study quantum quenches, and discuss the relation to the Sachdev-Ye-Kitaev model.

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Notes

  1. 1.

    A review of the group theory concepts mentioned here may for instance be found in Appendix B of [13].

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Acknowledgements

I am very grateful to my collaborators Mario Flory, Carlos Hoyos, Max-Niklas Newrzella, Andy O’Bannon, Ioannis Papadimitriou, Jonas Probst and Jackson Wu.

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Authors and Affiliations

  1. Institut für Theoretische Physik und Astrophysik, Julius-Maximilians-Universität Würzburg, Würzburg, Germany

    Johanna Erdmenger

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  1. Johanna Erdmenger
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Correspondence to Johanna Erdmenger .

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Editors and Affiliations

  1. International Institute of Physics-UFRN, Natal-Rn, Rio Grande do Norte, Brazil

    Alvaro Ferraz

  2. Theory Division, Saha Institute of Nuclear Physics, Kolkata, India

    Kumar S. Gupta

  3. Department of Physics and Astronomy, University of British Columbia, Vancouver, BC, Canada

    Gordon Walter Semenoff

  4. International Institute of Physics-UFRN, Natal-Rn, Rio Grande do Norte, Brazil

    Pasquale Sodano

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Erdmenger, J. (2020). Holographic Kondo Models. In: Ferraz, A., Gupta, K., Semenoff, G., Sodano, P. (eds) Strongly Coupled Field Theories for Condensed Matter and Quantum Information Theory. Springer Proceedings in Physics, vol 239. Springer, Cham. https://doi.org/10.1007/978-3-030-35473-2_6

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