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.Comment: 11 pages, 14 figure
