Understanding strongly correlated quantum phenomena is a major ongoing challenge in condensed matter physics. This endeavor is hindered by difficulty in solving quantum many-body theories and the complexity of real materials. Two-dimensional moiré materials with remarkable tunability and flexibility stands out as a paradigmatic system for the simulation and investigation of strong correlation physics problems. In this talk, I will first introduce our recently developed technique where thermodynamic equation of states is detected using optical sensing. Applying this technique to a transition metal dichalcogenide (TMD) moiré system that realizes the Kane-Mele Hubbard model, we found an excitonic Chern insulator after a correlation driven topological phase transition. I will also discuss our recent observation of exciton Wigner crystal and exciton density wave phase in Coulomb-coupled flat-band system.
