Anderson localization in generalized discrete time quantum walks

TL;DR

This paper investigates Anderson localization phenomena in a generalized discrete time quantum walk model, revealing how disorder in specific parameters induces localization and providing analytical insights into localization length behavior.

Contribution

It introduces a generalized quantum walk framework with controllable parameters and analyzes how different types of disorder affect localization, including analytical expressions for localization length.

Findings

Disorder in potential and internal magnetic field energies induces Anderson localization.

Kinetic energy disorder causes logarithmic divergence of localization length at spectral symmetry points.

Analytical expressions for spectral-independent localization length are derived.

Abstract

We study Anderson localization in a generalized discrete time quantum walk - a unitary map related to a Floquet driven quantum lattice. It is controlled by a quantum coin matrix which depends on four angles with the meaning of potential and kinetic energy, and external and internal synthetic flux. Such quantum coins can be engineered with microwave pulses in qubit chains. The ordered case yields a two-band eigenvalue structure on the unit circle which becomes completely flat in the limit of vanishing kinetic energy. Disorder in the external magnetic field does not impact localization. Disorder in all the remaining angles yields Anderson localization. In particular, kinetic energy disorder leads to logarithmic divergence of the localization length at spectral symmetry points. Strong disorder in potential and internal magnetic field energies allows to obtain analytical expressions for spectrally independent localization length which is highly useful for various applications.