The GW Method: Basic Principles, Latest Developments and Its Applications for d- and f-Electron Systems

The many-body perturbation theory based on the Green's function provides a rigorous conceptual framework to describe ground-state and excited-state properties of materials The Green's function depends on the exchange-correlation self-energy, which is the solution of a set of complicated integro-differential equations, named Hedin's equations The method, which approximates the self-energy by its first-order term in terms of the screened Coulomb interaction (W), is currently the most accurate first-principles approach to describe quasi-particle electronic band structure properties of extended systems In this review, we first give an overview of the many-body perturbation theory for quasi-particle excitations based on the Green's function and screened Coulomb interaction The latest methodological developments are reviewed with an attempt to put different newly proposed schemes in a unified framework The current status of the method, in particular for d/f-electron systems, is illustrated by a few prototypical examples