Imprints of information scrambling on eigenstates of a quantum chaotic system

TL;DR

This paper explores how information scrambling patterns in quantum many-body systems are reflected in the eigenstates of the system's evolution operator, revealing detailed structures of quantum chaos.

Contribution

It introduces a unified framework linking eigenstate correlations to various measures of information scrambling, with exact results for a minimal quantum chaos model.

Findings

Eigenstate correlations encode information lightcone and butterfly effect

Finer structures of scrambling are revealed within the lightcone

Eigenstates reflect the full spatiotemporal dynamics of quantum chaos

Abstract

How are the spatial and temporal patterns of information scrambling in locally interacting quantum many-body systems imprinted on the eigenstates of the system's time-evolution operator? We address this question by identifying statistical correlations among sets of minimally four eigenstates that provide a unified framework for various measures of information scrambling. These include operator mutual information and operator entanglement entropy of the time-evolution operator, as well as more conventional diagnostics such as two-point dynamical correlations and out-of-time-ordered correlators. We demonstrate this framework by deriving exact results for eigenstate correlations in a minimal model of quantum chaos -- Floquet dual-unitary circuits. These results reveal not only the butterfly effect and the information lightcone, but also finer structures of scrambling within the lightcone. Our work thus shows how the eigenstates of a chaotic system can encode the full spatiotemporal anatomy of quantum chaos, going beyond the descriptions offered by random matrix theory and the eigenstate thermalisation hypothesis.