Bekenstein-Hawking Entropy and Strange Metals

TL;DR

This paper explores the connection between non-Fermi liquid models with variable charge density and entropy, and extremal charged black holes, revealing a precise match in their correlators and thermodynamic properties.

Contribution

It demonstrates a detailed correspondence between fermionic models with infinite-range interactions and AdS$_2$ black hole horizons, linking entropy, charge, and spectral asymmetry.

Findings

Correlators match those of extremal charged black holes' horizons.

Entropy density relates to Bekenstein-Hawking entropy and black hole thermodynamics.

Microscopic entropy computed without supersymmetry.

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.