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Holographic Fermi Surfaces and Entanglement Entropy

Noriaki Ogawa, Tadashi Takayanagi, Tomonori Ugajin

TL;DR

This paper argues that purely classical gravity duals cannot realize Landau Fermi liquids in 2+1 dimensions by linking Fermi surfaces to a logarithmic violation of the entanglement entropy area law. By combining holographic entanglement entropy with the null energy condition, the authors derive a bound on the low-temperature specific heat, $C \propto T^{\alpha}$ with $\alpha \le 2/3$, implying non-Fermi liquid behavior in any such dual. They construct an effective Einstein-Maxwell-scalar gravity model that yields the required IR structure $g(z)\sim (z/z_F)^2$ and demonstrate how this IR behavior produces the desired entanglement entropy and thermodynamics, including embeddings into asymptotically AdS spaces. The work clarifies how holographic Fermi surfaces can arise in a classical gravity regime and provides explicit IR solutions and scaling relations tying entanglement, thermodynamics, and IR geometry together.

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.

Holographic Fermi Surfaces and Entanglement Entropy

TL;DR

This paper argues that purely classical gravity duals cannot realize Landau Fermi liquids in 2+1 dimensions by linking Fermi surfaces to a logarithmic violation of the entanglement entropy area law. By combining holographic entanglement entropy with the null energy condition, the authors derive a bound on the low-temperature specific heat, with , implying non-Fermi liquid behavior in any such dual. They construct an effective Einstein-Maxwell-scalar gravity model that yields the required IR structure and demonstrate how this IR behavior produces the desired entanglement entropy and thermodynamics, including embeddings into asymptotically AdS spaces. The work clarifies how holographic Fermi surfaces can arise in a classical gravity regime and provides explicit IR solutions and scaling relations tying entanglement, thermodynamics, and IR geometry together.

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.

Paper Structure

This paper contains 14 sections, 91 equations, 4 figures.

Table of Contents

  1. Introduction and Summary
  2. Fermi Surface and Entanglement Entropy
  3. Logarithmic Violation of Area Law
  4. Free Fermion Calculation
  5. Entanglement Entropy for 2D Free Massless Dirac Fermions
  6. Possible Holographic Duals with Fermi Surfaces
  7. Holographic Entanglement Entropy
  8. Circular Subsystems
  9. Null Energy Condition and Specific Heat
  10. Constraints on Specific Heat
  11. Effective Gravity Model
  12. Equation of Motions and General Solutions
  13. IR Solution with Logarithmic Entanglement Entropy
  14. Embedding into Asymptotically AdS Solutions

Figures (4)

  • Figure 1: The shape of the function $r(z)$ for $z_*=1$.
  • Figure 2: The finite part of $S_A$ (called $S^{fin}_A$) as a function $l$.
  • Figure 3: The profile of scalar potential $V(\phi)+2\Lambda$ for $z_F=k=1$ and $p=3$. The unit of the vertical axis is $1/R^2$. The initial condition of the scalar field is set to be $\phi(0)=0$.
  • Figure 4: The profile of $W(\phi)$ for $z_F=k=1$ and $p=3$. The unit of the vertical axis is $A^2/R^2$. The initial condition of the scalar field is set to be $\phi(0)=0$.