Entanglement growth during thermalization in holographic systems

By Hong Liu, S. J. Suh. 2013

257 citations recorded by the source corpus.

We derive in detail several universal features in the time evolution of entanglement entropy and other nonlocal observables in quenched holographic systems. The quenches are such that a spatially uniform density of energy is injected at an instant in time, exciting a strongly coupled CFT which eventually equilibrates. Such quench processes are described on the gravity side by the gravitational collapse of a thin shell that results in a black hole. Various nonlocal observables have a unified description in terms of the area of extremal surfaces of different dimensions. In the large distance limit, the evolution of an extremal surface, and thus the corresponding boundary observable, is controlled by the geometry around and inside the event horizon of the black hole, allowing us to identify regimes of pre-local- equilibration quadratic growth, post-local-equilibration linear growth, a memory loss regime, and a saturation regime with behavior resembling those in phase transitions. We also discuss possible bounds on the maximal rate of entanglement growth in relativistic systems.

Subfields: Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/1d544cd6dc3565982672af7c2760c72a2ab68962

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Citations in the corpus

Islands in cosmology (2020, unknown): “In the regime |tI | β, the function f is known to be quadratic in time [54, 55, 59, 76], sthf(δη, 0) ≈ bf (δη)(2) (|δη| β0) .”
On entanglement spreading in chaotic systems (2016, background): “In [8, 9] a saturation velocity cE = R/tS was introduced to characterize the saturation time; in this language cE = ṽB.”
On the time dependence of holographic complexity (2017, background): “Let us comment that similar violations are observed for the proposed bounds for the maximal rate of entanglement growth in relativistic systems [57, 58].”
Quantum extremal islands made easy. Part II. Black holes on the brane (2020, background): “13) is saturated at times just above the thermal scale for sufficiently straight entangling surfaces — this definition is well-defined in the sense that vent turns out to be independent of the shape of the entangling surface, provided it is sufficiently straight [100, 101].”
Localized shocks (2014, methodology): “These include two-sided correlation functions [1, 2, 3], mutual information and entropy [4, 5, 6], and the pullbackpushforward [7, 8] modification of the standard smearing function procedure [9, 10, 11, 12].”
Complexity and Shock Wave Geometries (2014, background): “2) can be used as a clock, but it reaches its maximum after a multiple of the light-crossing time [1][2].”