Constructing the AdS dual of a Fermi liquid: AdS black holes with Dirac hair

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Article

Abstract

We provide evidence that the holographic dual to a strongly coupled charged Fermi liquid has a non-zero fermion density in the bulk. We show that the pole-strength of the stable quasiparticle characterizing the Fermi surface is encoded in the AdS probability density of a single normalizable fermion wavefunction in AdS. Recalling Migdal’s theorem which relates the pole strength to the Fermi-Dirac characteristic discontinuity in the number density at ωF, we conclude that the AdS dual of a Fermi liquid is described by occupied on-shell fermionic modes in AdS. Encoding the occupied levels in the total spatially averaged probability density of the fermion field directly, we show that an AdS Reissner-Nordström black holein a theory with charged fermions has a critical temperature, at which the system undergoes a first-order transition to a black hole with a non-vanishing profile for the bulk fermion field. Thermodynamics and spectral analysis support that the solution with non-zero AdS fermion-profile is the preferred ground state at low temperatures.

Keywords

Black Holes in String Theory AdS-CFT Correspondence Holography and condensed matter physics(AdS/CMT) 

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Copyright information

© SISSA, Trieste, Italy 2011

Authors and Affiliations

  • Mihailo Čubrović
    • 1
  • Jan Zaanen
    • 1
  • Koenraad Schalm
    • 1
  1. 1.Institute Lorentz for Theoretical PhysicsLeiden UniversityLeidenThe Netherlands

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