Interaction-driven phases in a Dirac semimetal: Exact diagonalization results

The interaction-driven phases in the Dirac semimetal (SM) of the π-flux model on the 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. We find 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.