  We propose a general scheme for diagnosing interaction-driven topological
phases in the weak interaction regime using exact diagonalization (ED). The
scheme comprises the analysis of eigenvalues of the point-group operators for
the many-body eigenstates and the correlation functions for physical
observables to extract the symmetries of the order parameters and the
topological numbers of the underlying ground states at the thermodynamic limit
from a relatively small size system afforded by ED. As a concrete example, we
investigate the interaction effects on the half-filled spinless fermions on the
checkerboard lattice with a quadratic band crossing point. Numerical results
support the existence of a spontaneous quantum anomalous Hall phase purely
driven by a nearest-neighbor weak repulsive interaction, separated from a
nematic Mott insulator phase at strong repulsive interaction by a first-order
phase transition.
