Holographic Fermi Surfaces and Entanglement Entropy

TL;DR

This paper explores the holographic duals of Fermi liquids and non-Fermi liquids, using entanglement entropy and energy conditions to distinguish their properties and identify classical gravity duals.

Contribution

It demonstrates that classical gravity duals cannot represent Landau-Fermi liquids and constructs a dual for non-Fermi liquids with correct entanglement and thermodynamic behavior.

Findings

Landau-Fermi liquids lack classical gravity duals.

Entanglement entropy reveals Fermi surface presence.

Constructed gravity dual matches non-Fermi liquid properties.

Abstract

We argue that Landau-Fermi liquids do not have any gravity duals in the purely classical limit. We employ the logarithmic behavior of entanglement entropy to characterize the existence of Fermi surfaces. By imposing the null energy condition, we show that the specific heat always behaves anomalously. We also present a classical gravity dual which has the expected behavior of the entanglement entropy and specific heat for non-Fermi liquids.