Abstract
We examine models of fermions with infinite-range interactions which realize non-Fermi liquids with a continuously variable U(1) charge density $\mathcal{Q}$, and a non-zero entropy density $\mathcal{S}$ at vanishing temperature. Real time correlators of operators carrying U(1) charge $q$ at a low temperature $T$ are characterized by a $\mathcal{Q}$-dependent frequency $\omega_{\mathcal{S}} = (q \, T/\hbar) (\partial \mathcal{S}/\partial{\mathcal{Q}})$ which determines a spectral asymmetry. We show that the correlators match precisely with those of the AdS$_2$ horizons of extremal charged black holes. On the black hole side, the matching employs $\mathcal{S}$ as the Bekenstein-Hawking entropy density, and the laws of black hole thermodynamics which relate $(\partial{\mathcal{S}}/\partial{\mathcal{Q}})/(2 \pi)$ to the electric field strength in AdS$_2$. The fermion model entropy is computed using the microscopic degrees of freedom of a UV complete theory without supersymmetry.
Highlights
Holography provides us with powerful tools for investigating models of quantum matter without quasiparticle excitations
As we demonstrate in this paper, the above properties of the Sachdev and Ye (SY) state match precisely with the quantum theory holographically dual to extremal charged black holes with two-dimensional anti–de Sitter (AdS2) horizons [14,15,16,17]
A key observation in the holographic framework is that E, related to the electric field, obeys an important identity which follows from the laws of black hole thermodynamics where SBH is the Bekenstein-Hawking entropy density of the AdS2 horizon
Summary
Holography provides us with powerful tools for investigating models of quantum matter without quasiparticle excitations. A key observation in the holographic framework is that E, related to the electric field, obeys an important identity which follows from the laws of black hole thermodynamics where SBH is the Bekenstein-Hawking entropy density of the AdS2 horizon. The holographic link between the SY state and the AdS2 horizons of charged black branes has been conjectured earlier [25,26,27], based upon the presence of a nonvanishing zero-temperature entropy density and the conformal structure of correlators.
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