  We present an exactly solvable model for synthetic anyons carrying
non-Abelian flux. The model corresponds to a two-dimensional electron gas in a
magnetic field with a specific spin interaction term, which allows only fully
aligned spin states in the ground state; the ground state subspace is thus
two-fold degenerate. This system is perturbed with identical solenoids carrying
a non-Abelian gauge potential. We explore dynamics of the ground state as these
solenoids are adiabatically braided and show they behave as anyons with a
non-Abelian flux. Such a system represents a middle ground between the ordinary
Abelian anyons and the fully non-Abelian anyons.
