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

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