Holographic Evolution of Entanglement Entropy

TL;DR

This paper investigates the evolution of entanglement entropy during holographic equilibration in a 2D conformal field theory, revealing propagation velocity, local equilibration, and the role of apparent horizons using Vaidya geometry.

Contribution

It demonstrates how holographic techniques can model entanglement dynamics in non-equilibrium 2D systems, connecting gravitational collapse to quantum entanglement propagation.

Findings

Entanglement propagates at velocity v^2=1.

Equilibration occurs locally, not globally.

Apparent horizon influences entanglement entropy in late stages.

Abstract

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. 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.