  The interaction-driven phases in the Dirac semimetal (SM) of the $\pi-$ flux
model on square lattice are studied with nearest-(NN), next-nearest- (NNN) and
next-next-nearest-neighbor (NNNN) interactions using the exact diagonalization
method. We find that the NN interaction drives a phase transition from the SM
phase to a charge density wave insulator. In the presence of the NNN
interaction, the system becomes an anisotropic SM for small interactions and an
insulator with the stripe order for large ones. The NNNN interaction drives the
Dirac SM to a dimmerized insulator. The interplay of the NNN and NNNN
interactions is also studied. It is found that the NNNN interaction firstly
eliminates the effect of the NNN interaction and then develops its favorable
order. In the calculations, the signature of the interaction-driven quantum
anomalous Hall phase is not found.
