We consider time-dependent entanglement entropy (EE) for a 1+1 dimensional CFT in the presence of angular momentum and U(1) charge. The EE saturates, irrespective of the initial state, to the grand canonical entropy after a time large compared with the length of the entangling interval. We reproduce the CFT results from an AdS dual consisting of a spinning BTZ black hole and a flat U(1) connection. The apparent discrepancy that the holographic EE does not a priori depend on the U(1) charge while the CFT EE does, is resolved by the charge-dependent shift between the bulk and boundary stress tensors. We show that for small entangling intervals, the entanglement entropy obeys the first law of thermodynamics, as conjectured recently. The saturation of the EE in the field theory is shown to follow from a version of quantum ergodicity; the derivation indicates that it should hold for conformal as well as massive theories in any number of dimensions.
We study holographic entanglement entropy in dS/CFT and introduce time-like entanglement entropy in CFTs. Both of them take complex values in general and are related with each other via an analytical continuation. We argue that they are correctly understood as pseudo entropy. We find that the imaginary part of pseudo entropy implies an emergence of time in dS/CFT.
The time evolution of entanglement tracks how information propagates in interacting quantum systems. We study entanglement entropy in CFT$_2$ with a time-dependent Hamiltonian. We perturb by operators with time-dependent source functions and use the replica trick to calculate higher order corrections to entanglement entropy. At first order, we compute the correction due to a metric perturbation in AdS$_3$/CFT$_2$ and find agreement on both sides of the duality. Past first order, we find evidence of a universal structure of entanglement propagation to all orders. The central feature is that int…
Imposing T-duality in the renormalisation process of entanglement entropy leads to new relations between entanglement entropy counter-terms. T-duality is made explicit by means of the generalised metric of double field theory in the context of bulk-boundary duality. Double field theory in the bulk naturally provides the new relations between higher order quantum corrections to entanglement entropy as well as a systematic approach to understanding entanglement entropy renormalisation counter-terms. An analogue for Slavnov-Taylor identities for T-dual counter-terms of entanglement entropy is env…
From black hole thermodynamics, the Bekenstein bound has been proposed as a universal thermal entropy bound. It has been further generalized to an entanglement entropy bound which is valid even in a quantum system. In a quantumly entangled system, the non-negativity of the relative entropy leads to the entanglement entropy bound. When the entanglement entropy bound is saturated, a quantum system satisfies the thermodynamics-like law with an appropriately defined entanglement temperature. We show that the saturation of the entanglement entropy bound accounts for a universal feature of the entan…
We review classical results on holographic entanglement entropy utilizing the Hamilton-Jacobi approach. Possibility of using the entanglement entropy as a probe of confinement is shortly discussed in the context of lattice data.
In this paper we study the holographic entanglement entropy in a large N noncommutative gauge field theory with two $θ$ parameters by Ryu-Takayanagi prescription (RT-formula). We discuss what contributions the presence of noncommutativity will make to the entanglement entropy in two different circumstances: 1) a rectangular strip and 2) a cylinder. Since we want to investigate the entanglement entropy only, we will not be discussing the finite temperature case in which the entropy calculated by the area of minimal surface will largely be the thermal part rather than the entanglement part. We f…
In this paper, we study the bulk entanglement entropy evolution in conical BTZ black bole background using the heat kernel method. This is motivated by exploring the new examples where quantum corrections of entanglement entropy give the leading contribution. We find that in the large black hole limit the bulk entanglement entropy decreases under the double-trace deformation which is consistent with the holographic $c$ theorem and in the small black hole limit the bulk entanglement entropy increases under the double-trace deformation.
We calculate the expectation value of the Wilson line in the pure AdS$_3$ Einstein gravity theory and also the entanglement entropy in the boundary theory. Our one-loop calculation of entanglement entropy shows a shift of the central charge 26. Finally, we show that the Wilson line provides the equivalent description to the boundary entanglement entropy. This equivalence leads to a concrete example of the building of "minimum surface=entanglement entropy".
Holographic entanglement entropy quantities for a three-party system are considered, namely tripartite information, total correlation and secrecy monotone. A holographic approach with Vaidya-AdS is used to calculate time evolution of the entanglement entropy during non-equilibrium heating. We study time dependence of these three entropy quantities.
We study holographic entanglement entropy in spatially anisotropic field theory. We observe that for the background we consider in this paper, to a good approximation, the holographic entanglement entropy can be decomposed into two terms. One of them is the entanglement entropy of the isotropic field theory at fixed temperature and the other term is only a function of anisotropy parameter. Moreover, for large enough values of anisotropy parameter, our numerical results indicate that the entanglement entropy in the perpendicular direction to anisotropic direction is greater than the parallel ca…
We use gauge-gravity duality to compute entanglement entropy in a non-conformal background with an energy scale $Λ$. At zero temperature, we observe that entanglement entropy decreases by raising $Λ$. However, at finite temperature, we realize that both $\fracΛ{T}$ and entanglement entropy rise together. Comparing entanglement entropy of the non-conformal theory, $S_{A(N)}$, and of its conformal theory at the $UV$ limit, $ S_{A(C)}$, reveals that $S_{A(N)}$ can be larger or smaller than $S_{A(C)}$, depending on the value of $\fracΛ{T}$.
We introduce "Replicated Entanglement Entropy (REE)" as the entanglement entropy of a subspace in a replicated theory. We calculate this quantity by replicating the original theory in two steps along the same entangling region and taking the proper limit on the second replica number. The quantity has a clear physical meaning, a thermodynamic interpretation and a holographic dual.
Geometric entropy and time-like entanglement entropy on a rotating BTZ black hole
The Chinese University of Hong Kong (Shenzhen)（香港中文大学（深圳））；Beijing Institute of Mathematical Sciences and Applications（北京国际数学研究中心）；University of South China（南华大学）；Ningbo University（宁波大学）
We study the entanglement entropy of the vacuum in non-relativistic local theories with Galilean or Schrödinger symmetry. We clear some confusion in the literature on the free Schrödinger case. We find that with only positive $U(1)$ charge particles (states) and a unique zero $U(1)$ charge state (the vacuum) the entanglement entropy must vanish in that state.
We explore holographic entanglement entropy in ten-dimensional supergravity solutions. It has been proposed that entanglement entropy can be computed in such top-down models using minimal surfaces which asymptotically wrap the compact part of the geometry. We show explicitly in a wide range of examples that the holographic entanglement entropy thus computed agrees with the entanglement entropy computed using the Ryu-Takayanagi formula from the lower-dimensional Einstein metric obtained from reduction over the compact space. Our examples include not only consistent truncations but also cases in…
We study the holographic entanglement entropy in a (d+1)-dimensional boundary quantum field theory at both the zero and finite temperature. The phase diagrams for the holographic entanglement entropy at various temperatures are obtained by solving the entangled surfaces in the different homology. We also verify the Araki-Lieb inequality and illustrate the entanglement plateau.
The renormalization of entanglement entropy of quantum field theories is investigated in the simplest setting with a $λϕ^4$ scalar field theory. The 3+1 dimensional spacetime is separated into two regions by an infinitely flat 2-dimensional interface. The entanglement entropy of the system across the interface has an elegant geometrical interpretation using the replica trick, which requires putting the field theory on a curved spacetime background. We demonstrate that the theory, and hence the entanglement entropy, is renormalizable at order $λ$ once all the relevant operators up to dimension-…
The spherical entanglement entropy of higher--spin fields conjectured by Benedetti and Casini is shown to follow by extrapolation of already existing low spin expressions. The corresponding fermion formula is also exhibited.
Utilizing the holographic technique, we investigate how the entanglement entropy evolves along the RG flow. After introducing a new generalized temperature which satisfies the thermodynamics-like law even in the IR regime, we find that the renormalized entropy and the generalized temperature in the IR limit approach the thermal entropy and thermodynamic temperature of a real thermal system. This result implies that the microscopic quantum entanglement entropy in the IR region leads to the thermodynamic relation up to small quantum corrections caused by the quantum entanglement near the entangl…
We generalize the analysis of arXiv:1210.7244 to de Sitter space α-vacua and compute the entanglement entropy of a free scalar for the half-sphere at late time.
The relation between kinematic space metric and entanglement entropy provides us with a differential equation for entanglement entropy. For BCFT on upper half plane we solve this equation to obtain an expression for entanglement entropy consistent with known results in the literature. We also discuss how this relation can be used to recast the RG flow, under relevant deformations of a CFT, as a flow in the space of kinematic space metrics.
In this note we calculate the holographic entanglement entropy in the presence of a conformal interface for a geometric configuration in which the entangling region ${\cal A}$ lies on one side of the interface. For the supersymmetric Janus solution we find exact agreement between the holographic and CFT calculation of the entanglement entropy.
In this work, a canonical method to compute entanglement entropy is proposed. We show that for two-dimensional conformal theories defined in a torus, a choice of moduli space allows the typical entropy operator of the TFD to provide the entanglement entropy of the degrees of freedom defined in a segment and their complement. In this procedure, it is not necessary to make an analytic continuation from the Rényi entropy and the von Neumann entanglement entropy is calculated directly from the expected value of an entanglement entropy operator. We also propose a model for the evolution of the enta…
We studied the holographic entanglement entropy for a strip and sharp wedge entangling regions in momentum relaxation systems. In the case of strips, we found analytic and numerical results for the entanglement entropy and showed the effect on the minimal surface by the electric field. We also studied the entanglement entropy of wedges and confirmed that there is a linear change in the electric field. This change is proportional to the thermoelectric conductivity, $\barα$, that can be measured.
I show that the black hole entropy associated to an $AdS_2$ wormhole is an entanglement edge term related to a natural measure on the gauge group in the $SL(2)$ gauge theory formulation of $1+1d$ Jackiw-Teitelboim gravity. I comment on what the entropy appears to be counting.
In this work, we perturbatively calculate the modular Hamiltonian to obtain the entanglement entropy in a free fermion theory on a torus with three typical deforma- tions, e.g., T\bar{T} deformation, local bilinear operator deformation, and mass deformation. For T\bar{T} deformation, we find that the leading order correction of entanglement entropy is proportional to the expectation value of the undeformed modular Hamiltonian. As a check, in the high/low-temperature limit, the entanglement entropy coincides with that obtained by the replica trick in the literature. Following the same perturbat…
We explore the behaviour of renormalized entanglement entropy in a variety of holographic models: non-conformal branes; the Witten model for QCD; UV conformal RG flows driven by explicit and spontaneous symmetry breaking and Schrödinger geometries. Focussing on slab entangling regions, we find that the renormalized entanglement entropy captures features of the previously defined entropic c-function but also captures deep IR behaviour that is not seen by the c-function. In particular, in theories with symmetry breaking, the renormalized entanglement entropy saturates for large entangling region…
In this paper, we derive the universal (cut-off-independent) part of the holographic entanglement entropy in the noncommutative Yang-Mills theory and examine its properties in detail. The behavior of the holographic entanglement entropy as a function of a scale of the system changes drastically between large noncommutativity and small noncommutativity. The strong subadditivity inequality for the entanglement entropies in the noncommutative Yang-Mills theory is modified in large noncommutativity. The behavior of entropic $c$-function defined by means of the entanglement entropy also changes dra…
We consider a conformal field theory in two dimensions in which an external perturbation is placed. We study the energy flux and entanglement entropy for one, two and multiple intervals and give a suggestion relating the two in some cases. We show that both the energy flux and the entanglement entropy exhibit a light-cone singularity which strongly depends on the regularization we choose.
We show that Schwarzschild black hole metrics are, asymptotically, Weyl equivalent to $AdS_2 \times S^{D-2}$ where the spherical factor is the horizon. The holographic entanglement entropy of $AdS_2$ exactly reproduces the Schwarzschild black hole entropy which implies that black hole degrees of freedom live at asymptotic infinity. In generalized theories of gravity, the same procedure reproduces Wald entropy.
This is the second part of two papers where we study the effect of integrable line defects on bipartite entanglement entropy in integrable field theories. In this paper, we consider non-topological line defects in Ising field theory. We derive an infinite series expression for the entanglement entropy and show that both the UV and IR limits of the bulk entanglement entropy are modified by the line defect. In the UV limit, we give an infinite series expression for the coefficient in front of the logarithmic divergence and the exact defect $g$-function. By tuning the defect to be purely transmis…
We analyze how excitations affect the entanglement entropy for an arbitrary entangling interval in a 2d conformal field theory (CFT) using the holographic entanglement entropy techniques as well as direct CFT computations. We introduce the excitation entanglement entropy Δ_h S, the difference between the entanglement entropy generic excitations and their arbitrary descendants denoted by h. The excitation entanglement entropy, unlike the entanglement entropy, is a finite quantity (independent of the cutoff), and hence a good physical observable. We show that the excitation entanglement entropy …
We investigate entanglement entropy in a scalar field theory on the fuzzy sphere. The theory is realized by a matrix model. In our previous study, we confirmed that entanglement entropy in the free case is proportional to the square of the boundary area of a focused region. Here we argue that this behavior of entanglement entropy can be understood by the fact that the theory is regularized by matrices, and further examine the dependence of entanglement entropy on the matrix size. In the interacting case, by performing Monte Carlo simulations, we observe a transition from a generalized volume l…
