  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.
