Dynamical Localization and Transport properties of Quantum Walks on the hexagonal lattice

Abstract

We study coined Random Quantum Walks on the hexagonal lattice, where the strength of disorder is monitored by the coin matrix. Each lattice site is equipped with an i.i.d. random variable that is uniformly distributed on the torus and acts as a random phase in every step of the QW. We show exponential decay of the fractional moments of the Green function in the regime of strong disorder, that is whenever the coin matrix is sufficiently close to the fully localized case, using a fractional moment criterion and a finite volume method. In the decorrelated case, we deduce dynamical localization. Moreover, we adapt a topological index to our model and thereby obtain transport for some coin matrices.