  We study the Mott phases and the superfluid-insulator transition of
two-component ultracold bosons on a square optical lattice in the presence of a
non-Abelian synthetic gauge field, which renders a SU(2) hopping matrix for the
bosons. Using a resummed hopping expansion, we calculate the excitation spectra
in the Mott insulating phases and demonstrate that the superfluid-insulator
phase boundary displays a non-monotonic dependence on the gauge field strength.
We also compute the momentum distribution of the bosons in the presence of the
non-Abelian field and show that they develop peaks at non-zero momenta as the
superfluid-insulator transition point is approached from the Mott side.
Finally, we study the superfluid phases near the transition and discuss the
induced spatial pattern of the superfluid density due to the presence of the
non-Abelian gauge potential.
