Quantum embedding theories for electron-boson coupled systems

We developed a canonical transformation based quantum embedding theory for electron-boson coupled problems. The method is applied to several electron-boson coupled systems, including the Hubbard-Holstein model and ab initio materials. In particular, we studied the modification of phase boundaries / reaction barriers via the formation of polarons or polaritons in an optical cavity. We show that the method gives accurate energies and observables comparable to exact diagonalization or DMRG calculations, and allows for large-scale simulations for quantum materials with modest computational cost.