Universal Anderson localization in one-dimensional unitary maps

Ihor Vakulchyk; Sergej Flach

doi:10.1063/5.0141808

Universal Anderson localization in one-dimensional unitary maps

Chaos. 2023 Aug 1;33(8):083134. doi: 10.1063/5.0141808.

Authors

Ihor Vakulchyk^{1

2}, Sergej Flach^{1

2}

Affiliations

¹ Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS), Daejeon 34126, Republic of Korea.
² Basic Science Program, Korea University of Science and Technology (UST), Daejeon 34113, South Korea.

PMID: 38060770
DOI: 10.1063/5.0141808

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.