Calculation of the GW self-energy in semiconducting crystals

The concepts of quasiparticle and collective excitation are considered in the context of continued-fraction expansions. This leads to a practical scheme allowing a highly accurate description of the screened interaction function W and the electron self-energy Σ, which can be achieved at a reasonable computational cost. The usefulness of this scheme is demonstrated on a simple two-band model of a semiconductor, where it leads to an unambiguous calculation of the electron self-energy in the GW approximation. Conceptually, the theory clarifies some of the limitations of the standard quasiparticle concept in many-body theory. Furthermore, it allows a proper assessment of the quality of the standard approximations employed in GW calculations.