Systematic Improvability in Quantum Embedding for Real Materials

Quantum embedding methods have become a powerful tool to overcome of traditional quantum modelling in materials science. However, these are systematically improvable in principle, in practice it is possible to achieve rigorous convergence and often necessary to employ parameters. Here, we formulate a quantum embedding theory, building the methods of density-matrix embedding theory combined with local approaches from quantum chemistry, to ensure the ability to converge properties of real materials with accurate correlated~function methods, controlled by a single, rapidly convergent parameter. By supercell size, basis set, and the resolution of the fluctuation of an embedded fragment, we show that the systematic improvability of the yields accurate structural and electronic properties of realistic without empirical parameters, even across changes in geometry. Results presented in insulating, semi-metallic, and more strongly correlated, finding state of the art agreement to experimental data.