  Non-interacting topological states of matter can be realized in band
insulators with intrinsic spin-orbital couplings as a result of the nontrivial
band topology. In recent years, the possibility of realizing novel
interaction-driven topological phase has attracted a lot of research
activities, which may significantly extend the classes of topological states of
matter. Here, we report a new finding of an interaction-driven spontaneous
quantum Hall effect (QHE) (Chern insulator) emerging in an extended
fermion-Hubbard model on kagome lattice. By means of the state-of-the-art
density-matrix renormalization group, we expose universal properties of the QHE
including time-reversal symmetry spontaneous breaking and quantized Hall
conductance. By accessing the ground state in large systems, we demonstrate the
robustness of the QHE against finite-size effects. Moreover, we map out a phase
diagram and identify two competing charge density wave phases by varying
interactions, where transitions to the QHE phase are determined to be of the
first order. Our study provides a "proof-of-the-principle" demonstration of
interaction-driven QHE without requirement of external magnetic field or
magnetic doping.
