Self-consistent GW for a quasi-one-dimensional semiconductor

We present self-consistent GW calculations for a quasi-one-dimensional model semiconductor, using multipole representations for W, the screened interaction, and G, the electron Green function. In the case of G, we distinguish between the quasiparticle contribution and the so-called incoherent contribution. We consider various strengths of the external potential. For two different starting points of the self-consistency cycle, local-density approximation and Hartree-Fock, the band gaps converge to the same values. The self-consistent GW band gaps differ very little from the Hartree-Fock band gaps. There is considerable disagreement with quantum Monte Carlo calculations for the same model, indicating the importance of vertex correction