Holographic Entanglement Entropy and Fermi Surfaces

TL;DR

This paper investigates holographic models of Fermi surfaces, revealing a specific geometry with a null curvature singularity and proposing a nonsingular model to study zero-temperature Fermi surface physics.

Contribution

It identifies a unique nonsingular holographic geometry for Fermi surfaces and analyzes the nature of singularities and string excitations in these models.

Findings

The geometry exhibits a null curvature singularity except at a specific critical exponent.

Strings become infinitely excited near the singularity, indicating a potential 'stringularity'.

A nonsingular Einstein-Maxwell-dilaton geometry is constructed as a model for Fermi surface studies.

Abstract

The entanglement entropy in theories with a Fermi surface is known to produce a logarithmic violation of the usual area law behavior. We explore the possibility of producing this logarithmic violation holographically by analyzing the IR regions of the bulk geometries dual to such theories. The geometry of Ogawa, Takayanagi, and Ugajin is explored and shown to have a null curvature singularity for all values of parameters, except for dynamical critical exponent 3/2 in four dimensions. The results are extended to general hyperscaling violation exponent. We explore strings propagating through the singularity and show that they become infinitely excited, suggesting the singularity is not resolved by stringy effects and may become a full-fledged "stringularity." An Einstein-Maxwell-dilaton embedding of the nonsingular geometry is exhibited where the dilaton asymptotes to a constant in the IR. The unique nonsingular geometry in any given number of dimensions is proposed as a model to study the T=0 limit of a theory with a Fermi surface.