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We investigate the topological quantum phase transition (TQPT)of Fermi gases trapped in a honeycomb lattice in the presence of a synthetic non-Abelian gauge potential.We provide a scheme to use minimal number of Wilson loops tocharacterize the gauge invariant properties of the system.We develop a systematic fermionic effective field theory (EFT) to describe a topological quantum phase transition tuned by thenon-Abelian gauge potential and explore its various important experimental consequences.