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arXiv · 1506.05111

Bekenstein-Hawking Entropy and Strange Metals

Subir Sachdev
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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.

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Subir Sachdev. 2015-06-16. Bekenstein-Hawking Entropy and Strange Metals. https://doi.org/10.1103/physrevx.5.041025

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