  By the spin-fermion formula, the Hubbard model on the honeycomb lattice is
represented by a U(2) gauge theory in the mean field method, non-Abelian vortex
solutions are constructed based on this theory. The quantization condition
shows that the magnetic flux quanta are half-integer. There are $2k$ bosonic
zero modes for $k$ winding vortices. For the fermions, there are 2 zero energy
states (ZESs) corresponding to the single elementary vortex. In the vortex core
and on the edge, the system are in the semi-metal phase with a spin gap and in
the insulator phase with N\'eel order phase, and can be mapped to the
superconductor in class A and CI, respectively.
