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We study the out-of-time-order correlation (OTOC) of the Floquet transverseIsing model and use it to verify the phase diagram of the system. First, wepresent the exact analytical solution of the transverse magnetization OTOCusing the Jorden-Wigner transformation. We calculate the speed of correlationpropagation and analyze the behavior of the revival time with the separationbetween the observables. In order to get the phase structure of the Floquettransverse Ising system, we use the longitudinal magnetization OTOC as it isknown to serve as an order parameter of the system. We show the phase structurenumerically in the transverse Ising Floquet system by using the long timeaverage of the longitudinal magnetization OTOC. In both the open and the closedchain systems, we find distinct phases out of which two are paramagnetic(0-paramagnetic and $\pi$-paramagnetic), and two are ferromagnetic(0-ferromagnetic and $\pi$-ferromagnetic) as defined in the literature.

Out-of-time-order correlation and detection of phase structure in Floquet transverse Ising spin system