Information propagation and equilibration in long-range Kitaev chains

TL;DR

This paper investigates how information propagates in a long-range Kitaev chain, revealing ballistic information spread despite violations of traditional bounds, and highlights the impact of interaction range on information sharing and equilibration.

Contribution

It demonstrates that information still propagates ballistically in long-range Kitaev chains and explains this behavior through quasi-particle velocities, despite violations of Lieb-Robinson bounds.

Findings

Information propagates ballistically despite long-range interactions.

Interaction range significantly affects mutual information decay.

Local observables equilibrate very slowly.

Abstract

We study the propagation of information through a Kitaev chain with long-range pairing interactions. Although the Lieb-Robinson bound is violated in the strict sense for long-range interacting systems, we illustrate that a major amount of information in this model still propagates ballistically on a light cone. We find a pronounced effect of the interaction range on the decay of the mutual information between spatially disconnected subsystems. A significant amount of information is shared at time-like separations. This regime is accompanied by very slow equilibration of local observables. As the Kitaev model is quasi-free, we illustrate how the distribution of quasi-particle group velocities explains the physics of this system qualitatively.