Quasiparticle calculations in solids

This chapter provides an overview of quasiparticle calculations in solids, and, in particular, the GW approximation (GWA). A successful approximation for the determination of excited states of solids is based on the quasiparticle concept and the Green function method. The Coulomb repulsion between electrons leads to a depletion of negative charge around a given electron, and the ensemble of this electron and its surrounding positive screening charge forms a quasiparticle. The mathematical description of quasiparticles is based on the single-particle Green function (G), whose exact determination requires complete knowledge of the quasiparticle self-energy ∑. The self-energy ∑ is a non-Hermitian, energy-dependent, nonlocal operator that describes exchange and correlation effects beyond the Hartree approximation. A determination of the self-energy can only be approximate, and a working scheme for the quantitative calculation of excitation energies in metals, semiconductors, and insulators is the so-called dynamically screened interaction or the GWA. The chapter also discusses (1) the physics and extensions of the GWA; (2) numerical aspects of GWA calculations; (3) applications of the GWA to semiconductors, insulators and metals; and (4) the relevance of GWA calculations to optical response. Finally, the chapter presents parallel algorithms both for reciprocal and real-space/imaginary-time GWA calculations and several alternative methods to determine excited states of solids within density functional theory.