Information Trapping by Topologically Protected Edge States: Scrambling and the Butterfly Velocity

Abstract: Topological insulators and superconductors have attracted considerable attention, and many different theoretical tools have been used to gain insight into their properties. Here we investigate how perturbations can spread through exemplary one-dimensional topological insulators and superconductors using out-of-time ordered correlators. Out-of-time ordered correlators are often used to consider how information becomes scrambled during quantum dynamics. The wavefront of the out-of-time ordered correlator can be ballistic regardless of the underlying system dynamics, and here we confirm that for topological free fermion systems the wavefront spreads linearly at a characteristic butterfly velocity. We pay special attention to the topologically protected edge states, finding that "information" can become trapped in the edge states and essentially decoupled from the bulk, surviving for relatively long times. We consider different models with multiple possible edge states coexisting on a single edge.