Ab initio calculations of quasiparticle band structure in correlated systems: LDA++ approach

TLDR: In this article, a general approach to a realistic theory of the electronic structure in materials containing correlated $d$ or $f$ electrons is discussed, taking into account of the energy dependence of the electron self-energy with the momentum dependence being neglected (local approximation).

Abstract: We discuss a general approach to a realistic theory of the electronic structure in materials containing correlated $d$ or $f$ electrons. The main feature of this approach is the taking into account of the energy dependence of the electron self-energy with the momentum dependence being neglected (local approximation). It allows us to consider such correlation effects as the non-Fermi-step form of the distribution function, the enhancement of the effective mass including Kondo resonances,'' the appearance of the satellites in the electron spectra, etc. To specify the form of the self-energy, it is useful to distinguish (according to the ratio of the on-site Coulomb energy $U$ to the bandwidth $W$) three regimes---strong, moderate, and weak correlations. In the case of strong interactions ($U/Wg1$---rare-earth system) the Hubbard-I approach is the most suitable. Starting from an exact atomic Green function with the constrained density matrix ${n}_{{\mathrm{mm}}^{\ensuremath{'}}}$ the band-structure problem is formulated as the functional problem on ${n}_{{\mathrm{mm}}^{\ensuremath{'}}}$ for $f$ electrons and the standard local-denisty-approximation functional for delocalized electrons. In the case of moderate correlations ($U/W\ensuremath{\sim}1$---metal-insulator regime, Kondo systems) we start from the $d=\ensuremath{\infty}$ dynamical mean-field iterative perturbation scheme of Kotliar and co-workers and also make use of our multiband atomic Green function for constrained ${n}_{{\mathrm{mm}}^{\ensuremath{'}}}$. Finally for the weak interactions ($U/Wl1$---transition metals) the self-consistent diagrammatic fluctuation-exchange approach of Bickers and Scalapino is generalized to the realistic multiband case. We present two-band, two-dimensional model calculations for all three regimes. A realistic calculation in the Hubbard-I scheme with the exact solution of the on-site multielectron problem for $f(d)$ shells was performed for mixed-valence $4f$ compound TmSe, and for the classical Mott insulator NiO.