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

The out-of-time-order correlator (OTOC) measures the propagation and scrambling of local quantum information. For the transverse field Ising model with open boundaries, the local operator σˣ shows an interesting picture of the ground state OTOC where the local information alternately gets scrambled and then ``unscrambled'' upon reflection at the ends. Earlier discussions of OTOCs did not explain the physical processes responsible for such scrambling and unscrambling. We explicitly show that in the paramagnetic phase, the scrambling and unscrambling is due to the scattering of a pair of low-energy spin-flip excitations, and extend it to incorporate integrability-breaking interactions. In the ferromagnetic phase these are explained by the motion of a domain-wall excitation, and we find that unscrambling survives up to moderate values of interactions. Thus, in different limits of the system parameters, we provide a simple understanding of the OTOCs, including the unscrambling, in terms of the low-energy excitations like spin flips or domain walls. We mention a system where our results can be experimentally tested.