Systems with purely off-diagonal disorder have peculiar features such as thelocalization-delocalization transition and long-range correlations in theirwavefunctions. To motivate possible experimental studies of the physics ofoff-diagonal disorder, we study in detail disordered discrete-time quantum walkin a finite chain, where the diagonal disorder can be set to zero byconstruction. Starting from a transfer matrix approach, we show, boththeoretically and computationally, that the dynamics of the quantum walk withdisorder manifests all the main features of off-diagonal disorder. We alsopropose how to prepare a remarkable delocalized zero-mode from a localized andeasy-to-prepare initial state using an adiabatic protocol that increases thedisorder strength slowly. Numerical experiments are also performed withencouraging results.
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