Quantum Information Scrambling in Quantum Many-body Scarred Systems

TL;DR

This paper investigates quantum information scrambling in many-body scarred systems, revealing unique light cone structures and oscillations in the PXP model, with implications for quantum simulation and understanding non-thermal eigenstates.

Contribution

It introduces a numerical method to analyze information scrambling in scarred systems and demonstrates measurable signatures in Rydberg-atom experiments.

Findings

OTOC and Holevo information show linear light cone and oscillations in scarred systems

Distinct scrambling behavior compared to thermal or localized systems

Proposes experimental measurement strategies for quantum simulators

Abstract

Quantum many-body scarred systems host special non-thermal eigenstates that support periodic revival dynamics and weakly break the ergodicity. Here, we study the quantum information scrambling dynamics in quantum many-body scarred systems, with a focus on the "PXP" model. We use the out-of-time-ordered correlator (OTOC) and Holevo information as measures of the information scrambling, and apply an efficient numerical method based on matrix product operators to compute them up to 41 spins. We find that both the OTOC and Holevo information exhibit a linear light cone and periodic oscillations inside the light cone for initial states within the scarred subspace, which is in sharp contrast to thermal or many-body localized systems. The periodic revivals of OTOCs and Holevo information signify unusual breakdown of quantum chaos and are not equivalent to the revival dynamics of state fidelity or local observables studied in the previous literature. To explain the formation of the linear light cone structure, we provide a perturbation-type calculation based on a phenomenological model. In addition, we demonstrate that the OTOC and Holevo information dynamics of the "PXP" model can be measured using the Rydberg-atom quantum simulators with current experimental technologies, and numerically identify the measurable signatures using experimental parameters.