  The method of synthetic gauge potentials opens up a new avenue for our
understanding and discovering novel quantum states of matter. We investigate
the topological quantum phase transition of Fermi gases trapped in a honeycomb
lattice in the presence of a synthetic non- Abelian gauge potential. We develop
a systematic fermionic effective field theory to describe a topological quantum
phase transition tuned by the non-Abelian gauge potential and ex- plore its
various important experimental consequences. Numerical calculations on lattice
scales are performed to compare with the results achieved by the fermionic
effective field theory. Several possible experimental detection methods of
topological quantum phase tran- sition are proposed. In contrast to condensed
matter experiments where only gauge invariant quantities can be measured, both
gauge invariant and non-gauge invariant quantities can be measured by
experimentally generating various non-Abelian gauges corresponding to the same
set of Wilson loops.
