Anderson localization in generalized discrete-time quantum walks

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. Suc...

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Bibliographic Details
Published in:Physical review. B 2017-10, Vol.96 (14), Article 144204
Main Authors: Vakulchyk, I., Fistul, M. V., Qin, P., Flach, S.
Format: Article
Language:English
Subjects:
Anderson localization
Coins
Divergence
Eigenvalues
Kinetic energy
Localization
Magnetic fields
Mathematical analysis
Qubits (quantum computing)
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Summary: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 one to obtain analytical expressions for spectrally independent localization length, which is highly useful for various applications.
ISSN:2469-9950
2469-9969
DOI:10.1103/PhysRevB.96.144204