Correlation matrix renormalization theory in multi-band lattice systems.

An appropriate treatment of electronic correlation effects plays an important role in accurate descriptions of physical and chemical properties of real materials. The recently proposed Correlation Matrix Renormalization theory with Sum Rule correction (CMR) for studying correlated electron materails has shown good performance in molecular systems and a periodic Hydrogen chain in comparison with various quantum chemistry and quantum Monte Carlo calculations. This work gives a detailed formulation and computational code implementation of CMR in multi-band periodic lattice systems. This lattice CMR ab initio theory is highly efficient, has no material specific adjustable parameters, and has no double counting issues faced by the hybrid approaches like LDA+U, DFT+DMFT and DFT+GA type theories. Benchmark studies on materials with s and p orbitals in this study show that CMR in its current implementation consistently performs well for these systems as the electron correlation increases from the bonding region to the bond breaking region.