Operator growth and eigenstate entanglement in an interacting integrable Floquet system

TL;DR

This paper studies an interacting integrable Floquet system, revealing that despite its integrability, it exhibits operator growth similar to chaotic models and shows unique entanglement properties in eigenstates.

Contribution

It demonstrates that an integrable Floquet model can display operator growth and eigenstate entanglement behaviors typically associated with chaotic systems.

Findings

Operator commutators grow diffusively, similar to chaotic models.

Eigenstate thermalization hypothesis (ETH) holds for local operators.

Large subsystems violate ETH, with entanglement saturating below half-system size.

Abstract

We analyze a simple model of quantum dynamics, which is a discrete-time deterministic version of the Frederickson-Andersen model. We argue that this model is integrable, with a quasiparticle description related to the classical hard-rod gas. Despite the integrability of the model, commutators of physical operators grow as in generic chaotic models, with a diffusively broadening front, and local operators obey the eigenstate thermalization hypothesis (ETH). However, large subsystems violate ETH; as a function of subsystem size, eigenstate entanglement first increases linearly and then saturates at a scale that is parametrically smaller than half the system size.