Constructing the AdS dual of a Fermi liquid: AdS black holes with Dirac hair
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.
KeywordsBlack Holes in String Theory AdS-CFT Correspondence Holography and condensed matter physics(AdS/CMT)
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