Universal scaling of quantum state transport in a one-dimensional topological chain under nonadiabatic dynamics

When a system is driven across a continuous phase transition, the density of topological defects demonstrates a power-law scaling behavior versus the quenching rate, as predicted by the Kibble-Zurek mechanism. In this study, we generalize this idea and address the scaling of quantum state transport in a one-dimensional topological system subject to a linear drive through its topological quantum phase transition point. We illustrate the power-law dependences of the quantum state's transport distance, width, and peak magnitude on the driving velocity. Crucially, the power-law exponents are distinct for the edge state and bulk state. Our results offer a different perspective on quantum state transfer and enrich the field of Kibble-Zurek behaviors and nonadiabatic quantum dynamics.