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Journal of High Energy Physics

, 2013:86 | Cite as

A holographic model of the Kondo effect

  • Johanna Erdmenger
  • Carlos Hoyos
  • Andy O’BannonEmail author
  • Jackson Wu
Article

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.

Keywords

Holography and condensed matter physics (AdS/CMT) Gauge-gravity correspondence AdS-CFT Correspondence 

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Copyright information

© The Author(s) 2013

Authors and Affiliations

  • Johanna Erdmenger
    • 1
  • Carlos Hoyos
    • 2
  • Andy O’Bannon
    • 3
    • 4
    Email author
  • Jackson Wu
    • 5
  1. 1.Max-Planck-Institut für Physik (Werner-Heisenberg-Institut)MünchenGermany
  2. 2.Raymond and Beverly Sackler School of Physics and AstronomyTel-Aviv UniversityRamat-AvivIsrael
  3. 3.Department of Applied Mathematics and Theoretical PhysicsUniversity of CambridgeCambridgeUnited Kingdom
  4. 4.Rudolf Peierls Centre for Theoretical PhysicsUniversity of OxfordOxfordUnited Kingdom
  5. 5.National Center for Theoretical Sciences, Physics DivisionHsinchuChina

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