Holographic Entanglement Entropy and Hidden Fermi surfaces

TL;DR

This paper demonstrates the existence of classical gravity duals for Fermi and non-Fermi liquids using entanglement entropy behavior, revealing insights into their thermodynamic properties and proposing an effective gravity model for anisotropic systems.

Contribution

It provides a proof of classical gravity duals for Fermi liquids via entanglement entropy analysis and introduces an effective gravity model for anisotropic backgrounds.

Findings

Logarithmic entanglement entropy indicates Fermi surfaces in gravity duals.

Specific heat scales as $C\propto T^\alpha$ with $\alpha\leq1$ under null energy condition.

Multiple solutions for anisotropic systems' minimal surfaces are identified.

Abstract

We prove that the purely classical gravity dual of Fermi and non-Fermi liquids exist by employing the logarithmic behavior of entanglement entropy to probe Fermi surfaces. For isotropic systems, the logarithmic behavior originates only from UV-IR intermediate regions of the minimal area surface. For anisotropic systems, the surfaces' configuration becomes largely modified by spatial anisotropy and series of solutions exist. By imposing the null energy condition we show that the specific heat behaves as $C\propto T^\alpha$ where $\alpha\leq1$, in both systems. In the end, we also present an effective gravity modle for anisotropic background.