A covariant holographic entanglement entropy proposal

Abstract

With an aim towards understanding the time-dependence of entanglement entropy in generic quantum field theories, we propose a covariant generalization of the holographic entanglement entropy proposal of hep-th/0603001. Apart from providing several examples of possible covariant generalizations, we study a particular construction based on light-sheets, motivated in similar spirit to the covariant entropy bound underlying the holographic principle. In particular, we argue that the entanglement entropy associated with a specified region on the boundary in the context of the AdS/CFT correspondence is given by the area of a co-dimension two bulk surface with vanishing expansions of null geodesics. We demonstrate our construction with several examples to illustrate its reduction to the holographic entanglement entropy proposal in static spacetimes. We further show how this proposal may be used to understand the time evolution of entanglement entropy in a time varying QFT state dual to a collapsing black hole background. Finally, we use our proposal to argue that the Euclidean wormhole geometries with multiple boundaries should be regarded as states in a non-interacting but entangled set of QFTs, one associated to each boundary.

Holographic geometry of cMERA for quantum quenches and finite temperature

“…To optimize this bound we need to choose γ A which minimizes the number of bonds. This prescription looks very similar to the holographic entanglement entropy [9][10][11][12][13], which is given by the minimal area divided by four times the Newton constant G N . This observation is a very important evidence of this conjecture.…”

“…This connection suggests that the spacetime in gravity can be regarded as collections of bits of quantum entanglement and explains the holographic entanglement entropy [9][10][11][12][13] in a very beautiful way. A closely related viewpoint has also been pointed out in [14,15].…”

“…As we mentioned we chose a particular θ k (t) by requiring that the diagonal elements of the matrix G(u) are vanishing and this corresponds to a particular time slice in the gravity dual geometry [16]. Therefore in general if we want to calculate S A using the holographic entanglement entropy [9][10][11][12][13], we need to know the correct extremal surface, which deviates from the time slice corresponding to a choice of θ k (t). Thus, strictly speaking, we need the time-like component g tt to find S A .…”

Quantum Entanglement Growth under Random Unitary Dynamics

“…This irreversible growth of entanglementquantified by the growth of the von Neumman entropyis important for several reasons. It is an essential part of thermalization, and as a result has been addressed in diverse contexts ranging from conformal field theory [1][2][3][4] and holography [5][6][7][8][9][10][11][12] to integrable [13][14][15][16][17][18][19], nonintegrable [20][21][22][23], and strongly disordered spin chains [24][25][26][27][28][29][30]. Entanglement growth is also of practical importance as the crucial obstacle to simulating quantum dynamics numerically, for example, using matrix product states or the density matrix renormalization group [31].…”

Non-equilibrium condensation process in holographic superconductor with nonlinear electrodynamics

“…The entanglement entropy is directly related to the degrees of freedom of a system to keep track of them. From [86,99,100], we can see in a time-dependent background the entanglement entropy associated with a specified region on the boundary in the context of the AdS/CFT correspondence is given by the area of a co-dimension two bulk surface with vanishing expansions of null geodesics. We will follow this treatment to calculate the entanglement entropy in the time-dependent background.…”