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

TL;DR

This paper constructs a holographic dual of a strongly coupled Fermi liquid using AdS black holes with fermionic hair, revealing a phase transition and the role of fermion density in the bulk.

Contribution

It demonstrates that a charged AdS black hole with fermionic hair models a Fermi liquid, showing a phase transition and linking quasiparticle properties to bulk fermion wavefunctions.

Findings

Identifies a critical temperature for phase transition to fermionic hair.

Shows the fermion density in AdS encodes Fermi liquid quasiparticle strength.

Confirms the non-zero fermion profile as the thermodynamically favored state at low temperatures.

Abstract

We provide new 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 spatially averaged 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 $\ome_F$, 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 probability density of the fermion field directly, we show that an AdS Reissner-Nordstr\"{o}m black hole in 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 confirm that the solution with non-zero AdS fermion-profile is the preferred ground state at low temperatures.