The GW method

TL;DR

The paper discusses the GW approximation, a key method in condensed matter physics for calculating excited-state properties of materials, including its theory, numerical methods, applications, and recent developments.

Contribution

It provides a comprehensive overview of the GW method, including its theoretical foundation, computational techniques, and recent advancements beyond the basic approximation.

Findings

The GW approximation is effective for excited-state calculations.

Numerical methods for self-energy calculations are detailed.

Recent developments improve accuracy and address limitations.

Abstract

Calculations of ground-state and excited-state properties of materials have been one of the major goals of condensed matter physics. Ground-state properties of solids have been extensively investigated for several decades within the standard density functional theory. Excited state properties, on the other hand, were relatively unexplored in ab initio calculations until a decade ago. The most suitable approach up to now for studying excited-state properties of extended systems is the Green function method. To calculate the Green function one requires the self-energy operator which is non-local and energy dependent. In this article we describe the GW approximation which has turned out to be a fruitful approximation to the self-energy. The Green function theory, numerical methods for carrying out the self-energy calculations, simplified schemes, and applications to various systems are described. Self-consistency issue and new developments beyond the GW approximation are also discussed as well as the success and shortcomings of the GW approximation.