Correlation renormalized and induced spin-orbit coupling


 Interplay of spin-orbit coupling (SOC) and electron correlation generates a bunch of emergent quantum phases and transitions, especially topological insulators (TI) and topological transitions. In this work, we find that electron correlation will induce extra large SOC in multi-orbital systems under atomic SOC and change ground state topological properties. Using Hartree-Fock mean field theory, phase diagrams of $p_{x}/p_{y}$ orbital ionic Hubbard model on honeycomb lattice are well studied. In general, correction of strength of SOC $\delta \lambda \propto (U'-J)$. Due to breaking down of rotation symmetry, form of SOC on multi-orbital materials are also changed under correlation. If non-interacting system is close to fermionic instability, spontaneous generalized SOC can also be found. Using renormalization group, SOC is leading instability close to quadratic band-crossing point. Mean fields at quadratic band-crossing point are also studied.