  We discuss the possibility of realizing metal-insulator transitions with
ultracold atoms in two-dimensional optical lattices in the presence of
artificial gauge potentials. Such transitions have been extensively studied for
magnetic fields corresponding to Abelian gauges; they occur when the magnetic
flux penetrating the lattice plaquette is an irrational multiple of the
magnetic flux quantum. Here we present the first study of these transitions for
non-Abelian U(2) gauge fields, which can be realized with atoms with two pairs
of degenerate internal states. In contrast to the Abelian case, the spectrum
and localization transition in the non-Abelian case is strongly influenced by
atomic momenta. In addition to determining the localization boundary, the
momentum fragments the spectrum and the minimum energy viewed as a function of
momentum exhibits a step structure. Other key characteristics of the
non-Abelian case include the absence of localization for certain states and
satellite fringes around the Bragg peaks in the momentum distribution and an
interesting possibility that the transition can be tuned by the atomic momenta.

Other Condensed Matter;Chaotic Dynamics