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We propose a general scheme for diagnosing interaction-driven topologicalphases in the weak interaction regime using exact diagonalization (ED). Thescheme comprises the analysis of eigenvalues of the point-group operators forthe many-body eigenstates and the correlation functions for physicalobservables to extract the symmetries of the order parameters and thetopological numbers of the underlying ground states at the thermodynamic limitfrom a relatively small size system afforded by ED. As a concrete example, weinvestigate the interaction effects on the half-filled spinless fermions on thecheckerboard lattice with a quadratic band crossing point. Numerical resultssupport the existence of a spontaneous quantum anomalous Hall phase purelydriven by a nearest-neighbor weak repulsive interaction, separated from anematic Mott insulator phase at strong repulsive interaction by a first-orderphase transition.

Diagnosis of interaction-driven topological phase via exact diagonalization