Entanglement Tsunami: Universal Scaling in Holographic Thermalization

TL;DR

This paper studies the universal behavior of entanglement entropy growth after a quench in holographic systems, revealing regimes of quadratic, linear, and saturation growth linked to black hole formation.

Contribution

It introduces the concept of an 'entanglement tsunami' to describe entanglement spreading and proposes a conjecture on the maximal entanglement growth rate in relativistic systems.

Findings

Identifies distinct regimes of entanglement growth: quadratic, linear, and saturation.

Shows that entanglement evolution is governed by black hole horizon geometry.

Proposes a universal scaling behavior in holographic thermalization.

Abstract

We consider the time evolution of entanglement entropy after a global quench in a strongly coupled holographic system, whose subsequent equilibration is described in the gravity dual by the gravitational collapse of a thin shell of matter resulting in a black hole. In the limit of large regions of entanglement, the evolution of entanglement entropy is controlled by the geometry around and inside the event horizon of the black hole, resulting in regimes of pre-local- equilibration quadratic growth (in time), post-local-equilibration linear growth, a late-time regime in which the evolution does not carry any memory of the size and shape of the entangled region, and a saturation regime with critical behavior resembling those in continuous phase transitions. Collectively, these regimes suggest a picture of entanglement growth in which an "entanglement tsunami" carries entanglement inward from the boundary. We also make a conjecture on the maximal rate of entanglement growth in relativistic systems.