Reentrant localization and mobility edges in a spinful Aubry-André-Harper model with a non-Abelian potential

We study localization properties and mobility edges of a generalized spinful Aubry-Andr\'e-Harper (AAH) model, which is the dimensional reduction of the two-dimensional Hofstadter model with a non-Abelian SU(2) gauge potential. Depending on whether the quasiperiod is comparable with the lattice size, the model has different localization properties. In the noncomparable case, the generalized AAH model still retains duality properties. Tuning the non-Abelian gauge can make the system undergo an unconventional reentrant localization phase transition as the strength of quasiperiodic potential increases. Furthermore, mobility edges exist in the mixed phase where the localized states sit at the center of spectra. Nevertheless, the non-Abelian gauge potential results in more mobility edges than that the Abelian gauge potential does, when the model is in the semiclassical limit where the quasiperiod is comparable with the lattice size. Moreover, exact expressions of the mobility edges and localization phase diagrams are analytically obtained by a semiclassical method.