Nonergodic Quantum Dynamics from Deformations of Classical Cellular Automata

TL;DR

This paper demonstrates that classical reversible cellular automata can generate nonergodic quantum dynamics with exact nonthermal eigenstates, providing a new link between classical chaos and quantum nonthermalization.

Contribution

It introduces a family of non-integrable, periodically-driven quantum systems derived from classical cellular automata, revealing their nonergodic and nonthermal eigenstates.

Findings

Classical CAs define quantum Floquet systems with exact nonthermal eigenstates.

Certain product states on classical orbits do not thermalize, indicating nonergodicity.

Potential for experimental probing in Rydberg atom quantum simulators.

Abstract

Classical reversible cellular automata (CAs), which describe the discrete-time dynamics of classical degrees of freedom in a finite state-space, can exhibit exact, nonthermal quantum eigenstates despite being classically chaotic. We show that every classical CA defines a family of generically non-integrable, periodically-driven (Floquet) quantum dynamics with exact, nonthermal eigenstates. These Floquet dynamics are nonergodic in the sense that certain product states on a periodic classical orbit fail to thermalize, while generic initial states thermalize as expected in a quantum chaotic system. We demonstrate that some signatures of these effects can be probed in quantum simulators based on Rydberg atoms in the blockade regime. These results establish classical CAs as parent models for a class of quantum chaotic systems with rare nonthermal eigenstates.