Interaction-Driven Spontaneous Quantum Hall Effect on Kagome Lattice

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.