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The spatiotemporal evolution of the out-of-time-order correlator (OTOC)measures the propagation and scrambling of local quantum information. For thetransverse field Ising model with open boundaries, the local operator$\sigma^{x}$ shows an interesting picture of the ground state OTOC where thelocal information gets scrambled throughout the entire system and, morestrikingly, starts `unscrambling' upon reflection at the other end. Earlierdiscussions of OTOCs did not explain the physical processes responsible forsuch scrambling and unscrambling of information. We explicitly show that in theparamagnetic phase, the scrambling and unscrambling is due to the scattering ofa pair of low-energy spin-flip excitations, even in the presence of smallinteractions. In the ferromagnetic phase the same phenomena are explained bythe motion of a domain-wall excitation. Thus, in different limits of the systemparameters, we have provided a simple and almost complete understanding of thespace-time pictures of the OTOCs, including the unscrambling, in terms of thelow-energy excitations like one and two spin-flips or a single domain wall.

Mechanisms of scrambling and unscrambling of quantum information in the  ground state in spin chains: domain-walls, spin-flips and scattering phase  shifts