The<b><i>GW</i></b>method

Abstract

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