Orbital Chern Insulator and Spontaneous Time Reversal Symmetry Breaking of Electron Systems with Partially Filled Energy Bands

 In this talk, I will present numerical evidendence of an interaction-driven spontaneous quantum Hall effect  emerging in  extended fermion-Hubbard models based on  state-of-the-art density-matrix renormalization group simulations. For  electrons on kagome lattice with half-filled lowest flat bands by considering the antiferromagnetic Heisenberg interaction (J) and short-range Coulomb interactions (V), I will discuss a quantum phase diagram and identify a fully spin-polarized phase. I will show that neighboring repulsions (V) drive a spontaneous chiral current, which makes the system an orbital Chern insulator characterized by a quantized Hall conductance.  We further  show that the orbital Chern insulator is robust against small antiferromagnetic coupling (J) while  a nonmagnetic phase with spin and charge nematicity appears at larger J.   At last, we will also demonstrate the effect of electron doping on frustrated systems to unveil the connection between spontaneous time reversal symmetry breaking and topological superconductivity.