Combining DFT and many-body methods to understand correlated materials

The electronic and magnetic properties of many strongly correlated systems are controlled by a limited number of states, located near the Fermi level and well isolated from the rest of the spectrum. This opens a formal way for combining the methods of first-principles electronic structure calculations, based on the density-functional theory (DFT), with many-body models, formulated in the restricted Hilbert space of states close to the Fermi level. The core of this project is the so-called ` realistic modeling' or the construction of the many-body model Hamiltonian entirely from first principles. Such a construction should be able to go beyond the conventional local-density approximation (LDA), which typically supplements the density-functional theory, and incorporate the physics of Coulomb correlations. It should also provide a transparent physical picture for the low-energy properties of strongly correlated materials. In this review article, we will outline the basic ideas of such a realistic modeling, which consists of the following steps: (i) the construction of the complete Wannier basis set for the low-energy LDA band; (ii) the construction of the one-electron part of the model Hamiltonian in this Wannier basis; (iii) the calculation of the screened Coulomb interactions for the low-energy bands by means of the constrained DFT. The most difficult part of this project is the evaluation of the screening caused by outer bands, which may have the same (e. g., the transition-metal 3d) character as the low-energy bands. The latter part can be efficiently done by combining the constrained DFT with the random-phase approximation (RPA) for the screened Coulomb interaction. The entire procedure will be illustrated on a series of examples, including the distorted transition-metal perovskite oxides, compounds with the inversion-symmetry breaking caused by the defects, and the alkali hyperoxide KO2, which can be regarded as an analog of strongly correlated systems where the localized electrons reside on the molecular orbitals of the O(2)(-)dimer. In order to illustrate the abilities of the realistic modeling, we will also consider solutions of the low-energy models obtained for a number of systems, and argue that it can be used as a powerful tool for the exploration and understanding of the properties of strongly correlated materials.