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, $\ensuremath{\theta}$. The same metric exhibits a logarithmic violation of the area law of entanglement entropy, as shown recently by Ogawa et al. [e-print arXiv:1111.1023 (unpublished)]. 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.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, $\ensuremath{\theta}$. The same metric exhibits a logarithmic violation of the area law of entanglement entropy, as shown recently by Ogawa et al. [e-print arXiv:1111.1023 (unpublished)]. 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.

arXiv:1112.0573Physical Review BJan 25, 2012399 citations

Holographic superconductors with hidden Fermi surfaces

Zhong-Ying Fan

In this paper, we investigate a holographic model of superconductor with hidden Fermi surfaces, which was defined by the logarithmic violation of area law of entanglement entropy. We works in fully back-reacted background using standard Einstein-Maxwell-Dilaton action with additional complex scalar filed which was charged under the Maxwell field. Particularly, we analyze the behavior of entanglement entropy during the phase transition. At the critical point, the finite part of the entanglement entropy has a discontinuity of slope and tends to a lower value in the superconducting phase all the way down to the zero temperature limit, indicating the reorganization of degrees of freedom of the system across the phase transition.In this paper, we investigate a holographic model of superconductor with hidden Fermi surfaces, which was defined by the logarithmic violation of area law of entanglement entropy. We works in fully back-reacted background using standard Einstein-Maxwell-Dilaton action with additional complex scalar filed which was charged under the Maxwell field. Particularly, we analyze the behavior of entanglement entropy during the phase transition. At the critical point, the finite part of the entanglement entropy has a discontinuity of slope and tends to a lower value in the superconducting phase all the way down to the zero temperature limit, indicating the reorganization of degrees of freedom of the system across the phase transition.

arXiv:1311.4110Nov 17, 20131 citation

Holographic Entanglement Entropy

Mukund Rangamani, Tadashi Takayanagi

Lecture notes in physicsJan 1, 2017187 citations

Holographic Entanglement Entropy and Hidden Fermi surfaces

Zhong-Ying Fan

We prove that the purely classical gravity dual of Fermi and non-Fermi liquids exist by employing the logarithmic behavior of entanglement entropy to probe Fermi surfaces. For isotropic systems, the logarithmic behavior originates only from UV-IR intermediate regions of the minimal area surface. For anisotropic systems, the surfaces' configuration becomes largely modified by spatial anisotropy and series of solutions exist. By imposing the null energy condition we show that the specific heat behaves as $C\propto T^α$ where $α\leq1$ , in both systems. In the end, we also present an effective gravity modle for anisotropic background.We prove that the purely classical gravity dual of Fermi and non-Fermi liquids exist by employing the logarithmic behavior of entanglement entropy to probe Fermi surfaces. For isotropic systems, the logarithmic behavior originates only from UV-IR intermediate regions of the minimal area surface. For anisotropic systems, the surfaces' configuration becomes largely modified by spatial anisotropy and series of solutions exist. By imposing the null energy condition we show that the specific heat behaves as $C\propto T^α$ where $α\leq1$, in both systems. In the end, we also present an effective gravity modle for anisotropic background.

arXiv:1303.3472Mar 14, 20131 citation

z

, and a specific hyperscaling violation exponent, $\ensuremath{\theta}$. The same metric exhibits a logarithmic violation of the area law of entanglement entropy, as shown recently by Ogawa et al. [e-print arXiv:1111.1023 (unpublished)]. 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.

C\propto T^α

where

α\leq1

, in both systems. In the end, we also present an effective gravity modle for anisotropic background.