Effect of interactions on two-dimensional Dirac fermions

Based on the two-dimensional $\pi$-flux model, we study the interaction effects both in nontrivial massive and massless Dirac fermions with the numerical exact diagonalization method. In the presence of the nearest and next-nearest neighbor interactions: For a nontrivial massive Dirac fermion, the topological phase is robust and persists in a finite region of the phase diagram; while for the massless Dirac fermion, charge-density wave and stripe phases are identified and the phase diagram in the (V1,V2) plane is obtained. When the next-next-nearest neighbor interaction is further included to massless Dirac fermion, the topological phase expected in the mean-field theory is absent. Our results are related to the possibility of dynamically generating a topological phase from the electronic correlations.