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We study characteristic, dynamic, and saturation regimes of theout-of-time-order correlation (OTOC) in the constant field Floquet system withand without longitudinal field. In the calculation of OTOC, we take local spinsin longitudinal and transverse directions as observables which are local andnon-local in terms of Jordan-Wigner fermions, respectively. We use the exactanalytical solution of OTOC for the integrable model (without longitudinalfield term) with transverse direction spins as observables and numericalsolutions for other integrable and nonintegrable cases. OTOCs generated in bothcases depart from unity at a kick equal to the separation between theobservables when the local spins in the transverse direction and one additionalkick is required when the local spins in the longitudinal direction. The numberof kicks required to depart from unity depends on the separation between theobservables and is independent of the Floquet period and system size. In thedynamic region, OTOCs show power-law growth in both models, the integrable(without longitudinal field) as well as the nonintegrable (with longitudinalfield). The exponent of the power-law increases with increasing separationbetween the observables. Near the saturation region, OTOCs grow linearly with avery small rate.

Characteristic, dynamic, and near saturation regions of Out-of-time-order correlation in Floquet Ising models