Hidden Fermi surfaces in compressible states of gauge-gravity duality

TL;DR

This paper demonstrates that certain holographic models with specific scaling properties can represent compressible metallic states with hidden Fermi surfaces, characterized by unique entanglement entropy behaviors and dependent on charge density and temperature.

Contribution

It introduces a class of holographic metrics with dynamic critical and hyperscaling exponents that model hidden Fermi surfaces in compressible states, supported by entanglement entropy analysis.

Findings

Logarithmic violation of entanglement entropy area law.

Dependence of entanglement entropy on shape, charge, and temperature.

Support for holographic description of metallic states with hidden Fermi surfaces.

Abstract

General scaling arguments, and the behavior of the thermal entropy density, are shown to lead to an infrared metric holographically representing a compressible state with hidden Fermi surfaces. This metric is characterized by a general dynamic critical exponent, z, and a specific hyperscaling violation exponent, \theta. The same metric exhibits a logarithmic violation of the area law of entanglement entropy, as shown recently by Ogawa et al. (arXiv:1111.1023). We study the dependence of the entanglement entropy on the shape of the entangling region(s), on the total charge density, on temperature, and on the presence of additional visible Fermi surfaces of gauge-neutral fermions; for the latter computations, we realize the needed metric in an Einstein-Maxwell-dilaton theory. All our results support the proposal that the holographic theory describes a metallic state with hidden Fermi surfaces of fermions carrying gauge charges of deconfined gauge fields.