# Holographic Fermi surfaces and entanglement entropy

```@article{Ogawa2012HolographicFS,
title={Holographic Fermi surfaces and entanglement entropy},
author={Noriaki Ogawa and Tadashi Takayanagi and Tomonori Ugajin},
journal={Journal of High Energy Physics},
year={2012},
volume={2012},
pages={1-21}
}```
• Published 4 November 2011
• Physics
• Journal of High Energy Physics
A bstractWe 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.
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## References

SHOWING 1-10 OF 56 REFERENCES
Entanglement entropy and the Fermi surface.
An intuitive account of this anomalous scaling based on a low energy description of the Fermi surface as a collection of one-dimensional gapless modes is given and a violation of the boundary law is predicted in a number of other strongly correlated systems.
Conformal field theory approach to Fermi liquids and other highly entangled states
The Fermi surface may be usefully viewed as a collection of (\$1+1\$)-dimensional chiral conformal field theories. This approach permits straightforward calculation of many anomalous ground-state
Non-Fermi liquids from holography
• Physics
• 2011
We report on a potentially new class of non-Fermi liquids in (2+1)-dimensions. They are identified via the response functions of composite fermionic operators in a class of strongly interacting
Violation of the entropic area law for fermions.
• M. Wolf
• Physics
Physical review letters
• 2006
It is proven that the presented scaling law holds whenever the Fermi surface is finite, and this is, in particular, true for all ground states of Hamiltonians with finite range interactions.
Holographic Derivation of Entanglement Entropy from AdS/CFT
• Physics
• 2006
A holographic derivation of the entanglement entropy in quantum (conformal) field theories is proposed from AdS/CFT correspondence. We argue that the entanglement entropy in d+1 dimensional conformal
Holographic Entanglement Entropy: An Overview
• Physics
• 2009
In this paper, we review recent progress on the holographic understanding of the entanglement entropy in the anti-de Sitter space/conformal field theory (AdS/CFT) correspondence. In general, the
Entanglement entropy of critical spin liquids.
• Physics
Physical review letters
• 2011
It is found that entanglement entropy of the projected Fermi sea state violates the boundary law, with S(2) enhanced by a logarithmic factor, an unusual result for a bosonic wave function reflecting the presence of emergent fermions.
Entanglement entropy and conformal field theory
• Physics
• 2009
We review the conformal field theory approach to entanglement entropy in 1+1 dimensions. We show how to apply these methods to the calculation of the entanglement entropy of a single interval, and
Conformal Field Theory on the Fermi Surface
The Fermi surface may be usefully viewed as a collection of 1 + 1 dimensional chiral conformal field theories. This approach permits straightforward calculation of many anomalous ground state
Entanglement Entropy of Fermi Liquids via Multidimensional Bosonization
• Physics
• 2011
The logarithmic violations of the area law, i.e. an "area law" with logarithmic correction of the form \$S \sim L^{d-1} \log L\$, for entanglement entropy are found in both 1D gapless system and for