Holographic evolution of entanglement entropy. (English) Zbl 1294.81128

Abajo-Arrastia, Javier; Aparício, João; López, Esperanza

J. High Energy Phys. 2010, No. 11, Paper No. 149, 27 p. (2010).

Summary: 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 \(v^{2} = 1\) [P. Calabrese and J. L. Cardy, “Evolution of entanglement entropy in one-dimensional systems”, J. Stat. Mech. Theory Exp. 2005, No. 4, Paper P04010, 4 p. (2005) arxiv:cond-mat/0503393]. 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.

MSC:

81T20	Quantum field theory on curved space or space-time backgrounds
81T40	Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
83C57	Black holes
81P40	Quantum coherence, entanglement, quantum correlations
94A17	Measures of information, entropy

Keywords:

AdS-CFT correspondence; field theories in lower dimensions; black holes

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