Vertex corrections in localized and extended systems

Abstract

Within many-body perturbation theory, we apply vertex corrections to various closed-shell atoms and to jellium, using a local approximation for the vertex consistent with starting the many-body perturbation theory from a Kohn-Sham Green's function constructed from density-functional theory in the local-density approximation. The vertex appears in two places-in the screened Coulomb interaction W and in the self-energy ⌺-and we obtain a systematic discrimination of these two effects by turning the vertex in ⌺ on and off. We also make comparisons to standard GW results within the usual random-phase approximation, which omits the vertex from both. When a vertex is included for closed-shell atoms, both ground-state and excited-state properties demonstrate little improvement over standard GW. For jellium, we observe marked improvement in the quasiparticle bandwidth when the vertex is included only in W, whereas turning on the vertex in ⌺ leads to an unphysical quasiparticle dispersion and work function. A simple analysis suggests why implementation of the vertex only in W is a valid way to improve quasiparticle energy calculations, while the vertex in ⌺ is unphysical, and points the way to the development of improved vertices for ab initio electronic structure calculations.

Neutral and charged excitations in carbon fullerenes from first-principles many-body theories

“…As a consequence of this cancellation, the contributions from LDA screening are often neglected in calculations of electronic gap in crystals [13]. In molecular systems, these contributions are not negligible because they affect IP and EA separately [15,33]. Selfconsistency has been found to systematically increase the electronic gap compared to nonself-consistent GW methodologies in a variety of different materials [13,34].…”

“…There is an ongoing debate in the literature concerning the importance of vertex corrections [13,15,33]. The GW f approximation has vertex corrections included in two ways:…”

Ab‐initio theory of semiconductor band structures: New developments and progress

“…For a more general discussion see Ref. [61]. We discuss the corresponding influences for one gKS starting point for compounds with shallow d-levels.…”

Exciting prospects for solids: Exact‐exchange based functionals meet quasiparticle energy calculations

“…Imposing selfconsistency in an approximate fashion [46,[48][49][50] is not unique and different methods yield different results. Since the controversies regarding self-consistency within GW have not been resolved conclusively yet, and research into vertex corrections is still in its infancy [51][52][53] the majority of all GW calculations is performed employing the zeroth order in the self-energy ( 0 0 G W ). This, however, introduces a dependence of the starting Green's function on the self-energy and thus the quasiparticle energies, which can have a noticeable influence, as we will demonstrate in this article.…”