  Ultracold Fermi gases trapped in honeycomb optical lattices provide an
intriguing scenario, where relativistic quantum electrodynamics can be tested.
Here, we generalize this system to non-Abelian quantum electrodynamics, where
massless Dirac fermions interact with effective non-Abelian gauge fields. We
show how in this setup a variety of topological phase transitions occur, which
arise due to massless fermion pair production events, as well as pair
annihilation events of two kinds: spontaneous and strongly-interacting induced.
Moreover, such phase transitions can be controlled and characterized in optical
lattice experiments.
