  The strong correlation effects on topological insulator are studied in a
two-sublattice system with an onsite single-particle energy difference $\Delta$
between two sublattices. At $\Delta=0$, increasing the onsite interaction
strength $U$ drives the transition from the quantum spin Hall insulating state
to the non-topological antiferromagnetic Mott-insulating (AFMI) state. When
$\Delta$ is larger than a certain value, a topologically trivial band insulator
or AFMI at small values of $U$ may change into a quantum anomalous Hall state
with antiferromagnetic ordering at intermediate values of $U$. Further
increasing $U$ drives the system back into the topologically trivial state of
AFMI. The corresponding phenomena is observable in the solid state and cold
atom systems. We also propose a scheme to realize and detect these effects in
cold atom systems.
