Significance of self-interaction corrections in the GW Γ method

Tawinan Cheiwchanchamnangij

Martin M. Rieger, Lutz Steinbeck, I.D. White +2 more

A L Kutepov

Self-consistent solutions of Hedin's equations (HE) for the two-site Hubbard model (HM) have been studied. They have been found for three-point vertices of increasing complexity (Γ = 1 (GW approximation), Γ1 from the first-order perturbation theory, and the exact vertex Γ(E)). Comparison is made between the cases when an additional quasiparticle (QP) approximation for Green's functions is applied during the self-consistent iterative solving of HE and when QP approximation is not applied. The results obtained with the exact vertex are directly related to the present open question-which approximation is more advantageous for future implementations, GW + DMFT or QPGW + DMFT. It is shown that in a regime of strong correlations only the originally proposed GW + DMFT scheme is able to provide reliable results. Vertex corrections based on perturbation theory (PT) systematically improve the GW results when full self-consistency is applied. The application of QP self-consistency combined with PT vertex corrections shows similar problems to the case when the exact vertex is applied combined with QP sc. An analysis of Ward Identity violation is performed for all studied in this work's approximations and its relation to the general accuracy of the schemes used is provided.

Yasutami Takada

On the basis of the self-consistent calculation scheme for the electron self-energy Σ with the use of the three-point vertex function Γ always satisfying the Ward identity, we find that the obtained quasi-particle dispersion in the normal state in gapped systems, such as semiconductors, insulators, and molecules, is well reproduced by that in the one-shot GW (or G0W0) approximation. In calculating the superconducting transition temperature Tc, we also find a similar situation; the result for Tc in the gauge-invariant self-consistent framework including the effect of Γ satisfying the Ward identity is different from that in the conventional Eliashberg theory (which amounts to the GW approximation for superconductivity) but is close to that in the G0W0 approximation. Those facts indicate that the G0W0 approximation actually takes proper account of both vertex and high-order self-energy corrections in a mutually cancelling manner and thus we can understand that the G0W0 approximation is better than the fully self-consistent GW one in obtaining some of physical quantities.

Arno Schindlmayr

Meng Wu, Zhenglu Li, Steven G. Louie