Abstract
In many-body perturbation theory (MBPT) the self-energy plays a key role since it contains all the many-body effects of the system. The exact self-energy is not known; as a first approximation one can set the vertex function to unity which leads to the GW approximation. The latter properly describes the high-density regime, where screening is important; in the low-density regime, instead, other approximations are proposed, such as the matrix, which describes multiple scattering between two particles. Here we combine the two approaches. Starting from the fundamental equations of MBPT, we show how one can derive the -matrix approximation to the self-energy in a common framework with . This allows us to elucidate several aspects of this formulation, including the origin of, and link between, the electron-hole and the particle-particle matrix, the derivation of a screened matrix, and the conversion of the matrix into a vertex correction. The exactly solvable Hubbard molecule is used for illustration.
- Received 17 June 2011
DOI:https://doi.org/10.1103/PhysRevB.85.155131
©2012 American Physical Society