LDA + DMFT Investigation of NiO

Introduction 1 INTRODUCTION From a microscopic ab-initio point of view, a solid material is an interacting many-particle system involving both ions and electrons. However, according to the Born-Oppenheimer approximation (Born and Oppenheimer, 1927), the ions and electrons can be treated separately. Indeed, many properties of solids can be well described by the electronic degree of freedom, while the ions only contribute through a static potential. The resultant electronic Hamiltonian is still far too complicated to be fully solved and immediately requires further approximations, among which the one-electron approximation plays an important role. Within this approximation, the electron-electron interaction is taken into account at a mean-field level, behaving like an effective potential, and therefore the many-electron problem reduces to a single-electron one described by a single-electron Schrödinger equation. Solving this Schrödinger equation leads to the energy band theory of solids. The effective potential can be determined in different ways, governed by different approximations, among which the Hartree-Fock (HF) approximation (Hartree, 1928; Fock, 1930) is the most famous example. At present the most satisfactory picture for single-electron theory is based on the density functional theory (DFT) (Hohenberg and Kohn, 1964) through Kohn-Sham's approach (Kohn and Sham, 1965). The single-particle approximation is very successfull for explaining the properties of weakly correlated systems, e.g., simple metals, ordinary insulators and some semiconductors, but generally fails for systems with strongly correlated electrons such as Mott insulators, cuprates, manganites and rare earth systems. A satisfactory description of these systems requires an explicit treatment of the interactions between electrons. The problem of understanding the properties of strongly correlated materials is one of the main challenges for modern condensed matter physics. In this case one has to go beyond the one-electron approximation and employ more sophisticated treatment of electron-electron interaction. For that purpose, practically one has to restrict oneself to the most important orbitals so that the many-electron interactions can be explicitly treated. For instance, the valence d electrons are the most relevant ones responsible for the properties of transition metal compounds, and a model Hamiltonian can be formulated involving only these electrons. The simplest model appropriate for the strongly correlated electrons is one-band Hub-bard model (Gutzwiller, 1963; Hubbard, 1963), in which only the on-site Coulomb 2 Introduction interaction is considered, whereas the long-range ones are neglected. However, it turned out even for such a highly simplified model it is still very difficult to solve, and the exact solution …