Uniform Anderson Localization in One-Dimensional Floquet Maps

Abstract

We study Anderson localization in a discrete-time quantum map dynamics in one dimension with nearest-neighbor hopping strength $\theta$ 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 $L_{loc}$. We present an exact theory for the calculation of the localization length as a function of the hopping, $1/L_{\text{loc}}=\left|\ln \left(|\sin (\theta )|\right)\right|$, that is tunable between zero and infinity by variation of the hopping $\theta$.