Out-of-time-order correlators of nonlocal block-spin and random observables in integrable and nonintegrable spin chains

TL;DR

This paper investigates out-of-time-order correlators in spin chains, revealing power-law growth and exponential saturation behaviors, and highlights the equivalence between OTOC and operator entanglement entropy in these systems.

Contribution

It introduces the study of OTOC for nonlocal block-spin and random observables in both integrable and nonintegrable spin chains, showing their saturation behaviors and connection to operator entanglement.

Findings

OTOC shows power-law growth in both regimes

Exponential saturation of OTOC occurs after scrambling time

OTOC equals operator entanglement entropy for random observables

Abstract

Out-of-time-order correlators (OTOC) in the Ising Floquet system, that can be both integrable and nonintegrable is studied. Instead of localized spin observables, we study contiguous symmetric blocks of spins or random operators localized on these blocks as observables. We find only power-law growth of OTOC in both integrable and nonintegrable regimes. In the non-integrable regime, beyond the scrambling time, there is an exponential saturation of the OTOC to values consistent with random matrix theory. This motivates the use of "pre-scrambled" random block operators as observables. A pure exponential saturation of OTOC in both integrable and nonintegrable system is observed, without a scrambling phase. Averaging over random observables from the Gaussian unitary ensemble, the OTOC is found to be exactly same as the operator entanglement entropy, whose exponential saturation has been observed in previous studies of such spin-chains.