Holographic evolution of entanglement entropy

By Javier Abajo-Arrastia, J. Aparício, Esperanza Lopez. 2010

357 citations recorded by the source corpus.

We study the evolution of entanglement entropy in a 2-dimensional equilibration process that has a holographic description in terms of a Vaidya geometry. It models a unitary evolution in which the field theory starts in a pure state, its vacuum, and undergoes a perturbation that brings it far from equilibrium. The entanglement entropy in this set up provides a measurement of the quantum entanglement in the system. Using holographic techniques we recover the same result obtained before from the study of processes triggered by a sudden change in a parameter of the hamiltonian, known as quantum quenches. Namely, entanglement in 2-dimensional conformal field theories propagates with velocity v2 = 1 [1]. Both in quantum quenches and in the Vaidya model equilibration is only achieved at the local level. Remarkably, the holographic derivation of this last fact requires information from behind the apparent horizon generated in the process of gravitational collapse described by the Vaidya geometry. In the early stages of the evolution the apparent horizon seems however to play no relevant role with regard to the entanglement entropy. We speculate on the possibility of deriving a thermalization time for occupation numbers from our analysis.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/2e55305c072babbb5793b00c4912f7bd99a9f15c

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Citations in the corpus

Evolution of holographic entanglement entropy after thermal and electromagnetic quenches (2010, background): “The idea of the holographic quench studied in [8, 20] (see also [25]) is that the system is simply”
Black holes and the butterfly effect (2013, methodology): “Mutual information and entanglement entropy have been used to diagnose thermalization after a quantum quench, in both conventional [14, 15] and holographic setups [7, 16, 17, 18, 19, 20, 21, 22].”
Extremal surfaces as bulk probes in AdS/CFT (2012, methodology): “(Also in specific Vaidya-type collapse situations, it has been seen explicitly [38] that geodesics can probe past the apparent horizon while being anchored on the boundary.”
Entanglement entropy from a holographic viewpoint (2012, background): “In this way, we can conclude that during a black hole formulation, the microscopic entropy does not increase [117, 119].”
Black hole collapse in the 1/c expansion (2016, methodology): “Interestingly, these observables ‘see’ the geometry behind both the event horizon and the apparent horizon of the collapsing black hole [45, 46].”
Holographic thermalization with chemical potential (2012, background): “If we identify kμ = δμv, then we get[32] T ext μν ∼ kμkν , with k(2) = 0 , (4.”
Random Quantum Circuits (2022, background): “However, efforts to understand out-of-equilibrium dynamics in lattice models (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17) quantum field theories (18, 19, 20, 21), and black holes (22, 23, 24, 25, 26) have shown that universal structures can emerge in quantum correlations and in the pa”
Causality & holographic entanglement entropy (2014, background): “However, since entanglement entropy is a more nonlocal quantity, which according to HRT is captured by a bulk surface that can go behind event and apparent horizons [15, 16] and penetrate into causally disconnected regions from the boundary, it is far less obvious whether CFT causality will survive ”
Strong subadditivity and the covariant holographic entanglement entropy formula (2012, background): “As noted in [7], an interesting feature is that some of the geodesics pass behind the horizon; in other words, accordng to HRT the entanglement entropies of some boundary intervals depend on the metric in the region behind the horizon.”