Dynamics of Holographic Entanglement Entropy Following a Local Quench

TL;DR

This paper investigates how entanglement entropy evolves after a local quench in holographic 2+1 dimensional CFTs, revealing propagation along a light-cone and different equilibration speeds.

Contribution

It demonstrates the propagation of entanglement following a local quench in holographic systems and characterizes the bounds on its speed, highlighting differences from non-holographic models.

Findings

Entanglement propagates along an emergent light-cone.

Propagation speed is bounded between the entanglement tsunami velocity and the speed of light.

Entanglement entropy reverts to equilibrium exponentially fast.

Abstract

We discuss the behaviour of holographic entanglement entropy following a local quench in 2+1 dimensional strongly coupled CFTs. The entanglement generated by the quench propagates along an emergent light-cone, reminiscent of the Lieb-Robinson light-cone propagation of correlations in non-relativistic systems. We find the speed of propagation is bounded from below by the entanglement tsunami velocity obtained earlier for global quenches in holographic systems, and from above by the speed of light. The former is realized for sufficiently broad quenches, while the latter pertains for well localized quenches. The non-universal behavior in the intermediate regime appears to stem from finite-size effects. We also note that the entanglement entropy of subsystems reverts to the equilibrium value exponentially fast, in contrast to a much slower equilibration seen in certain spin models.