  The interaction-driven quantum anomalous Hall (QAH) insulator has been sought
for a long time in a Dirac semimetal with linear band touching points at the
Fermi level. By combining exact diagonalization, density matrix renormalization
group, and analytical methods, we study a spinless fermion system on the
checkerboard lattice with two fold rotational symmetry, which realizes two
Dirac band touching points in the absence of interaction. At weak coupling, the
Dirac semimetal is stable. At a finite density-density repulsive interaction,
we analyze possible symmetry broken states, and find that an QAH state is
stabilized when the interaction strength exceeds the energy scale controlling
the separation between the Dirac points. Through numerical simulations, we
verify the existence of the QAH phase with spontaneous time-reversal symmetry
breaking and quantized Chern number $C = 1$.
