Universal Anderson localization in one-dimensional unitary maps

Abstract

We study Anderson localization in discrete-time quantum map dynamics in one dimension with nearest-neighbor hopping strength θ and quasienergies located on the unit circle. We demonstrate that strong disorder in a local phase field yields a uniform spectrum gaplessly occupying the entire unit circle. The resulting eigenstates are exponentially localized. Remarkably this Anderson localization is universal as all eigenstates have one and the same localization length Lloc. We present an exact theory for the calculation of the localization length as a function of the hopping, 1/Lloc=|ln⁡(|sin⁡(θ)|)|, which is tunable between zero and infinity by variation of the hopping θ.