Topological phase transition and delocalization in a disordered quantum walk
Discrete time quantum walks are artificial, periodically driven systems that can be used to simulate topological phases of ordinary static Hamiltonians while also exhibiting novel topological phenomena. In this talk we will describe a one dimensional quantum walk in the presence of static disorder. In the clean case, this quantum walk is known to be characterized by a pair of topological invariants that determine the number of boundary states in the system. We show how this topological classification can be extended to the disordered case using a recent approach based on scattering matrices, and identify the topological invariants of the disordered quantum walk. Furthermore we show that while in the generic case all states exhibit Anderson localization, at a critical point between different topological phases certain eigenstates of the system at specific energies become delocalized even in the presence of strong disorder