Density Matrix Embedding Theory for Strongly Correlated Solids

Density matrix embedding theory (DMET) [Phys. Rev. Lett. 2012, 109, 186404] has offered a promising wave function-in-wave function embedding method to treat electron correlation for large and extended systems. DMET has been gaining some successes for several lattice models and molecular systems. Herein, we present an extension of DMET to treat strongly correlated periodic systems, namely pDMET. In our implementation, a unit cell is considered as an impurity embedded in the environment made up by other unit cells in the computational supercell. The Wannier functions, i.e. the real-space presentation of the wave function, are used to perform the embedding calculation. The correlation potential is augmented in the k-space one-electron Hamiltonian to self-consistently minimize the difference between the one-electron density matrix at the mean-field level and that at the high-level. We test our method using different quantum chemical solvers (e.g. FCI, DMRG-CI, CCSD) on variety of systems, such as one-dimensional structure (hydrogen chain), covalent crystal (crystalline silicon), and ionic crystal (magnesium oxide). Finally, we discuss the feasibility of extending the method to compute electronic band structures of materials.