Anomalous Dynamical Scaling at Topological Quantum Criticality

We study the nonequilibrium driven dynamics at topologically nontrivial quantum critical points (QCPs),and find that topological edge modes at criticality give rise to anomalous universal dynamical scaling behavior. By analyzing the driven dynamics of bulk and boundary order parameters at topologically distinct Ising QCPs, we demonstrate that, while the bulk dynamics remain indistinguishable and follow standard Kibble Zurek (KZ) scaling, the anomalous boundary dynamics is unique to topological criticality, and its explanation goes beyond the traditional KZ mechanism. To elucidate the unified origin of this anomaly, we further study the dynamics of defect production at topologically distinct QCPs in free-fermion models and demonstrate similar anomalous universal scaling exclusive to topological criticality. These findings establish the existence of anomalous dynamical scaling arising from the interplay between topology and driven dynamics, challenging standard paradigms of quantum critical dynamics.