Density Matrix Embedding Theory for Correlated Materials and Electron-Boson Coupled Systems

I will talk about an ab initio density matrix embedding framework for faithful simulations of correlated materials and electron-boson coupled systems. The first part includes the density matrix embedding theory (DMET) and its applications to high-temperature superconductors. The method allows for spin SU(2) and particle-number U(1) symmetry-breaking states such that the superconducting orders spontaneously emerge during the self-consistency. We directly computed the superconducting pairing order of several doped cuprate materials and structures. We found that we could correctly capture two well-known trends: the pressure effect, where the pairing order increases with intra-layer pressure, and the layer effect, where the pairing order varies with the number of copper-oxygen layers. In the second part of the talk, I will discuss 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 systems. 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.