Localization-delocalization transition in discrete-time quantum walks with long-range correlated disorder

Abstract

We study the effects of spatially long-range correlated phase disorder on the Hadamard quantum walk on a line. The shift operator is built to exhibit an intrinsic disorder distribution featuring long-range correlations. To impose such, we resort to fractional Brownian motion with power-law spectrum 1/k^{2α} with α≥0 being the exponent that controls the degree of correlations. We discuss the scaling behavior of the walker's wave packet and report a localization-delocalization transition controlled by α. We unveil two intermediate dynamical regimes between exponential localization and full delocalization.