Scrambling and entanglement spreading in long-range spin chains

TL;DR

This paper investigates how information scrambling and entanglement spread in long-range spin chains, revealing different behaviors in regular and chaotic regimes and highlighting exponential scrambling at a dynamical critical point.

Contribution

It uncovers the distinct dynamics of scrambling and entanglement in regular versus chaotic long-range spin chains, especially at a dynamical critical point.

Findings

Scrambling and entanglement dynamics differ significantly in regular and chaotic regimes.

Entanglement saturates and becomes multipartite after the Ehrenfest time.

Exponential scrambling occurs not only in chaos but also at a dynamical critical point.

Abstract

We study scrambling in connection to multipartite entanglement dynamics in regular and chaotic long-range spin chains, characterized by a well defined semi-classical limit. For regular dynamics, scrambling and entanglement dynamics are found to be very different: up to the Ehrenfest time they rise side by side departing only afterwards. Entanglement saturates and becomes extensively multipartite, while scrambling continues its growth up to the recurrence time. Remarkably, the exponential behaviour of scrambling emerges not only in the chaotic case, but also in the regular one, when the dynamics occurs at a dynamical critical point.