  We study the properties of an ultracold Fermi gas loaded in a square optical
lattice and subjected to an external and classical non-Abelian gauge field. We
calculate the energy spectrum of the system and show that the Dirac points in
the energy spectrum will remain quite stable under onsite interaction of
certain strength. Once the on-site interaction grows stronger than a critical
value, the Dirac points will no longer be stable and merge into a single hybrid
point. This mergence implies a quantum phase transition from a semimetallic
phase to a band insulator. The on-site interaction between ultracold fermions
could be conveniently controlled by Feshbach resonances in current experiments.
We proposed that this remarkable interaction induced mergence of Dirac points
may be observed in the ultracold fermi gas experiments.
