Information Scrambling and the Correspondence of Entanglement- and Operator Dynamics in Systems with Nonlocal Interactions

TL;DR

This paper investigates how nonlocal interactions affect quantum information scrambling in Ising models, revealing a slowdown in operator growth and providing insights relevant for quantum simulation and quantum gravity research.

Contribution

It uncovers the impact of nonlocal interactions on operator dynamics and entanglement growth, highlighting differences from existing models of fast scrambling.

Findings

Nonlocal interactions can slow operator size growth despite nonlinear lightcones.

A model for fast scrambling does not exhibit this slowdown, indicating different underlying mechanisms.

Operator dynamics show a connection to entanglement entropy evolution after a quantum quench.

Abstract

How fast quantum information scrambles such that it becomes inaccessible by local probes turns out to be central to various fields. Motivated by recent works on spin systems with nonlocal interactions, we study information scrambling in different variants of the Ising model. Our work reveals that nonlocal interactions can induce operator dynamics not precisely captured by out-of-time-order correlators (OTOCs). In particular, the operator size exhibits a slowdown in systems with generic powerlaw interactions despite a highly nonlinear lightcone. A recently proposed microscopic model for fast scrambling does not show this slowdown, which uncovers a distinct analogy between a local operator under unitary evolution and the entanglement entropy following a quantum quench. Our work gives new insights on scrambling properties of systems in reach of current quantum simulation platforms and complements results on possibly observing features of quantum gravity in the laboratory.