Topologically induced pre-scrambling and dynamical detection of topological phase transitions at infinite temperature*

Out-of-time-order correlators (OTOCs) measured at infinite temperature are well-established tools to study quantum chaos in quantum many-body systems as well as information properties of black holes. Here we report that infinite-temperature OTOCs could also directly probe quantum phase transitions at zero temperature in contrast to common intuition. We reveal the mechanism that allows OTOC to prioritize the low energy effects over strong thermal fluctuations at infinite temperature and find that the mechanism is driven by topological degeneracy and hence is highly universal and robust, as long as the underlying system can be formulated in 1D Majorana basis. Using the Majorana representation, we analytically and numerically show that the infinite-temperature OTOCs detect the presence of Majorana zero modes at the ends of the chain that is associated with 1D Z2 topological order. Such sensitivity to zero modes introduces a new time-scale to the dynamics of non-integrable systems where the information scrambling temporarily freezes, suggesting a restricted scrambling for the topologically-protected quantum information. We dub the phenomenon as topologically induced pre-scrambling.