Spread of entanglement for small subsystems in holographic CFTs

TL;DR

This paper develops an analytic perturbative method to study the early-time entanglement entropy evolution for small subsystems in holographic CFTs after a global quench, revealing new physical insights beyond the entanglement tsunami picture.

Contribution

It introduces a novel analytic expansion approach for small subsystems, highlighting differences from large interval dynamics and verifying previous numerical findings.

Findings

Entanglement growth rate is not causally constrained in this regime.

Approach to saturation is always continuous, independent of entangling surface shape.

Saturation time varies non-monotonically with chemical potential.

Abstract

We develop an analytic perturbative expansion to study the propagation of entanglement entropy for small subsystems after a global quench, in the context of the AdS/CFT correspondence. Opposite to the large interval limit, in this case the evolution of the system takes place at timescales that are shorter in comparison to the local equilibration scale and thus, different physical mechanisms govern the dynamics and subsequent thermalization. In particular, we show that the heuristic picture in terms of a "entanglement tsunami" does not apply in this regime. We find two crucial differences. First, that the instantaneous rate of growth of the entanglement is not constrained by causality, but rather its time average. And second, that the approach to saturation is always continuous, regardless the shape of the entangling surface. Our analytic expansion also enables us to verify some previous numerical results, namely, that the saturation time is non-monotonic with respect to the chemical potential. All of our results are pertinent to CFTs with a classical gravity dual formulation.