Showing papers by "Tadashi Takayanagi published in 2013"
TL;DR: It is argued that the entanglement entropy for a very small subsystem obeys a property which is analogous to the first law of thermodynamics when the authors excite the system, and this provides a universal relationship between the energy and the amount of quantum information.
Abstract: We argue that the entanglement entropy for a very small subsystem obeys a property which is analogous to the first law of thermodynamics when we excite the system. In relativistic setups, its effective temperature is proportional to the inverse of the subsystem size. This provides a universal relationship between the energy and the amount of quantum information. We derive the results using holography and confirm them in two-dimensional field theories. We will also comment on an example with negative specific heat and suggest a connection between the second law of thermodynamics and the strong subadditivity of entanglement entropy.
309 citations
TL;DR: In this paper, a free falling particle in an AdS space is used as a holographic model of local quenches and the time-evolution of holographic entanglement entropy is calculated.
Abstract: We propose a free falling particle in an AdS space as a holographic model of local quench. Local quenches are triggered by local excitations in a given quantum system. We calculate the time-evolution of holographic entanglement entropy. We confirm a logarithmic time-evolution, which is known to be typical in two dimensional local quenches. To study the structure of quantum entanglement in general quantum systems, we introduce a new quantity which we call entanglement density and apply this analysis to quantum quenches. We show that this quantity is directly related to the energy density in a small size limit. Moreover, we find a simple relationship between the amount of quantum information possessed by a massive object and its total energy based on the AdS/CFT.
264 citations
TL;DR: In this paper, the dynamics of entanglement entropy for weakly excited states in conformal field theories by using anti-de Sitter/conformal field theory (AdS/CFT) were studied.
Abstract: We study the dynamics of entanglement entropy for weakly excited states in conformal field theories by using anti-de Sitter/conformal field theory (AdS/CFT). This is aimed at a first step to finding a counterpart of the Einstein equation in CFT language. In particular, we point out that the entanglement entropy satisfies differential equations that directly correspond to the Einstein equation in several setups of AdS/CFT. We also define a quantity called entanglement density in higher dimensional field theories and study its dynamical property for weakly excited states in conformal field theories.
168 citations
TL;DR: In this paper, the authors studied the time evolution of continuous MERA under quantum quenches in free field theories and showed that it qualitatively agrees with its gravity dual given by a half of the AdS black hole spacetime.
Abstract: We study the time evolution of cMERA (continuous MERA) under quantum quenches in free field theories. We calculate the corresponding holographic metric using the proposal of arXiv:1208.3469 and confirm that it qualitatively agrees with its gravity dual given by a half of the AdS black hole spacetime, argued by Hartman and Maldacena in arXiv:1303.1080. By doubling the cMERA for the quantum quench, we give an explicit construction of finite temperature cMERA. We also study cMERA in the presence of chemical potential and show that there is an enhancement of metric in the infrared region corresponding to the Fermi energy.
93 citations
TL;DR: In this article, the change in entanglement entropy, for small but arbitrary fluctuations about a given state, and the constraints imposed on it by the perturbative Einstein equations, linearized about the corresponding bulk state, are analyzed.
Abstract: Entanglement entropy in a field theory, with a holographic dual, may be viewed as a quantity which encodes the diffeomorphism invariant bulk gravity dynamics. This, in particular, indicates that the bulk Einstein equations would imply some constraints for the boundary entanglement entropy. In this paper we focus on the change in entanglement entropy, for small but arbitrary fluctuations about a given state, and analyze the constraints imposed on it by the perturbative Einstein equations, linearized about the corresponding bulk state. Specifically, we consider linear fluctuations about BTZ black hole in 3 dimension, pure AdS and AdS Schwarzschild black holes in 4 dimensions and obtain a diffeomorphism invariant reformulation of linearized Einstein equation in terms of holographic entanglement entropy. We will also show that entanglement entropy for boosted subsystems provides the information about all the components of the metric with a time index.
75 citations
TL;DR: In this article, the authors carried out an extensive study of the holographic entanglement entropy for strip-shaped subsystems in AdS plane wave backgrounds and found that the results depend crucially on whether the strip is parallel or orthogonal to the energy current.
Abstract: AdS plane waves describe simple backgrounds which are dual to anisotropically excited systems with energy fluxes. Upon dimensional reduction, they reduce to hyperscaling violating spacetimes: in particular, the AdS
5 plane wave is known to exhibit logarithmic behavior of the entanglement entropy. In this paper, we carry out an extensive study of the holographic entanglement entropy for strip-shaped subsystems in AdS plane wave backgrounds. We find that the results depend crucially on whether the strip is parallel or orthogonal to the energy current. In the latter case, we show that there is a phenomenon analogous to a phase transition.
56 citations
TL;DR: In this paper, a class of non-local field theories whose ground state entanglement entropy follows a volume law is presented, as long as the size of subsystem is smaller than a certain scale.
Abstract: In this paper, we present a simple class of non-local field theories whose ground state entanglement entropy follows a volume law as long as the size of subsystem is smaller than a certain scale. We will confirm this volume law both from numerical calculations and from analytical estimation. This behavior fits nicely with holographic results for spacetimes whose curvatures are much smaller than AdS spaces such as those in the flat spacetime.
43 citations
TL;DR: In this article, the Strěda formula for the electric Hall conductivity is generalized to the thermal Hall conductivities in two-dimensional topological phases, and the authors apply this formula to the Majorana surface states of 3D topological superconductors and derive cross-correlated responses between the angular momentum and thermal polarization.
21 citations
TL;DR: In this article, a free falling particle in an AdS space is used as a holographic model of local quenches and the time-evolution of holographic entanglement entropy is calculated.
Abstract: We propose a free falling particle in an AdS space as a holographic model of local quench. Local quenches are triggered by local excitations in a given quantum system. We calculate the time-evolution of holographic entanglement entropy. We confirm a logarithmic time-evolution, which is known to be typical in two dimensional local quenches. To study the structure of quantum entanglement in general quantum systems, we introduce a new quantity which we call entanglement density and apply this analysis to quantum quenches. We show that this quantity is directly related to the energy density in a small size limit. Moreover, we find a simple relationship between the amount of quantum information possessed by a massive object and its total energy based on the AdS/CFT.
20 citations
TL;DR: In this paper, the change in entanglement entropy, for small but arbitrary fluctuations about a given state, and the constraints imposed on it by the perturbative Einstein equations, linearized about the corresponding bulk state, are analyzed.
Abstract: Entanglement entropy in a field theory, with a holographic dual, may be viewed as a quantity which encodes the diffeomorphism invariant bulk gravity dynamics. This, in particular, indicates that the bulk Einstein equations would imply some constraints for the boundary entanglement entropy. In this paper we focus on the change in entanglement entropy, for small but arbitrary fluctuations about a given state, and analyze the constraints imposed on it by the perturbative Einstein equations, linearized about the corresponding bulk state. Specifically, we consider linear fluctuations about BTZ black hole in 3 dimension, pure AdS and AdS Schwarzschild black holes in 4 dimensions and obtain a diffeomorphism invariant reformulation of linearized Einstein equation in terms of holographic entanglement entropy. We will also show that entanglement entropy for boosted subsystems provides the information about all the components of the metric with a time index.
5 citations
TL;DR: In this article, the authors explain an application of holographic entanglement entropy to Fermi surface physics and show that Landau-Fermi liquids do not have any gravity duals in the purely classical limit.
Abstract: In this paper, we will explain an application of holographic entanglement entropy to Fermi surface physics. These holographic arguments show that Landau–Fermi liquids do not have any gravity duals in the purely classical limit [N. Ogawa, T. Takayanagi and T. Ugajin, J. High Energy Phys.125, 1 (2012), arXiv:1111.1023 [hep-th]].