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Two-Point Functions in a Holographic Kondo Model

Two-Point Functions in a Holographic Kondo Model
Two-Point Functions in a Holographic Kondo Model
We develop the formalism of holographic renormalization to compute two-point functions in a holographic Kondo model. The model describes a (0 + 1)-dimensional impurity spin of a gauged SU(N ) interacting with a (1 + 1)-dimensional, large-N , strongly-coupled Conformal Field Theory (CFT). We describe the impurity using Abrikosov pseudo-fermions, and define an SU(N )-invariant scalar operator O built from a pseudo-fermion and a CFT fermion. At large N the Kondo interaction is of the form O†O, which is marginally relevant, and generates a Renormalization Group (RG) flow at the impurity. A second-order mean-field phase transition occurs in which O condenses below a critical temperature, leading to the Kondo effect, including screening of the impurity. Via holography, the phase transition is dual to holographic superconductivity in (1 + 1)-dimensional Anti-de Sitter space. At all temperatures, spectral functions of O exhibit a Fano resonance, characteristic of a continuum of states interacting with an isolated resonance. In contrast to Fano resonances observed for example in quantum dots, our continuum and resonance arise from a (0 + 1)-dimensional UV fixed point and RG flow, respectively. In the low-temperature phase, the resonance comes from a pole in the Green’s function of the form -i〈O〉2, which is characteristic of a Kondo resonance.
Erdmenger, Johanna
4d10384c-0ad3-49e6-bec3-e72308515b4b
Hoyos, Carlos
65bc37c2-67c7-44f0-8160-3cb7461adff6
O'Bannon, Andrew
f0c14b6c-5b74-4319-8432-f9eba1e20cf3
Papadimitriou, Ioannis
61aeb3c8-7ab7-44db-a3ee-846392b997ba
Probst, Jonas
79a41e05-0c37-4efd-844d-cda7815aa622
Wu, Jackson
eeb7a102-d9f6-473e-ace1-1bf7b3061005
Erdmenger, Johanna
4d10384c-0ad3-49e6-bec3-e72308515b4b
Hoyos, Carlos
65bc37c2-67c7-44f0-8160-3cb7461adff6
O'Bannon, Andrew
f0c14b6c-5b74-4319-8432-f9eba1e20cf3
Papadimitriou, Ioannis
61aeb3c8-7ab7-44db-a3ee-846392b997ba
Probst, Jonas
79a41e05-0c37-4efd-844d-cda7815aa622
Wu, Jackson
eeb7a102-d9f6-473e-ace1-1bf7b3061005

Erdmenger, Johanna, Hoyos, Carlos, O'Bannon, Andrew, Papadimitriou, Ioannis, Probst, Jonas and Wu, Jackson (2017) Two-Point Functions in a Holographic Kondo Model. Journal of High Energy Physics, 2017 (3), [39]. (doi:10.1007/JHEP03(2017)039).

Record type: Article

Abstract

We develop the formalism of holographic renormalization to compute two-point functions in a holographic Kondo model. The model describes a (0 + 1)-dimensional impurity spin of a gauged SU(N ) interacting with a (1 + 1)-dimensional, large-N , strongly-coupled Conformal Field Theory (CFT). We describe the impurity using Abrikosov pseudo-fermions, and define an SU(N )-invariant scalar operator O built from a pseudo-fermion and a CFT fermion. At large N the Kondo interaction is of the form O†O, which is marginally relevant, and generates a Renormalization Group (RG) flow at the impurity. A second-order mean-field phase transition occurs in which O condenses below a critical temperature, leading to the Kondo effect, including screening of the impurity. Via holography, the phase transition is dual to holographic superconductivity in (1 + 1)-dimensional Anti-de Sitter space. At all temperatures, spectral functions of O exhibit a Fano resonance, characteristic of a continuum of states interacting with an isolated resonance. In contrast to Fano resonances observed for example in quantum dots, our continuum and resonance arise from a (0 + 1)-dimensional UV fixed point and RG flow, respectively. In the low-temperature phase, the resonance comes from a pole in the Green’s function of the form -i〈O〉2, which is characteristic of a Kondo resonance.

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More information

Accepted/In Press date: 21 February 2017
e-pub ahead of print date: 7 March 2017
Published date: 7 March 2017
Organisations: Theory Group

Identifiers

Local EPrints ID: 406298
URI: http://eprints.soton.ac.uk/id/eprint/406298
PURE UUID: 5c0b7017-02d5-446a-a2d6-26dd9fd3c246
ORCID for Andrew O'Bannon: ORCID iD orcid.org/0000-0001-7862-783X

Catalogue record

Date deposited: 10 Mar 2017 10:44
Last modified: 26 Nov 2021 06:02

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Contributors

Author: Johanna Erdmenger
Author: Carlos Hoyos
Author: Andrew O'Bannon ORCID iD
Author: Ioannis Papadimitriou
Author: Jonas Probst
Author: Jackson Wu

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