Dynamically screened vertex correction to GW

Abstract

Diagrammatic perturbation theory is a powerful tool for the investigation of interacting many-body systems, the self-energy operator encoding all the variety of scattering processes. In the simplest scenario of correlated electrons described by the GW approximation for the electron self-energy, a particle transfers a part of its energy to neutral excitations. Higher-order (in screened Coulomb interaction W ) self-energy diagrams lead to improved electron spectral functions (SFs) by taking more complicated scattering channels into account and by adding corrections to lower order self-energy terms. However, they also may lead to unphysical negative spectral functions. The resolution of this difficulty has been demonstrated in our previous works. The main idea is to represent the self-energy operator in a Fermi golden rule form which leads to a manifestly positive definite SF and allows for a very efficient numerical algorithm. So far, the method has only been applied to the three-dimensional electron gas, which is a paradigmatic system, but a rather simple one. Here we systematically extend the method to two dimensions including realistic systems such as monolayer and bilayer graphene. We focus on one of the most important vertex function effects involving the exchange of two particles in the final state. We demonstrate that it should be evaluated with the proper screening and discuss its influence on the quasiparticle properties.

Low-Order Scaling G0W0 by Pair Atomic Density Fitting

“… 52 − 54 In the GW approximation, 51 , 55 this expansion is truncated after first order, which accounts for the major part of electron correlation. 46 , 54 , 56 , 57 The GW approximation makes MBPT computationally tractable, greatly improves over DFT for the description of single-particle excitations, 46 , 53 , 58 and also paves the way toward accurate optical spectra using the Bethe-Salpeter equation formalism. 59 , 60 Large numbers of computational material science codes 48 , 56 , 61 − 72 feature GW implementations, and also in the quantum chemistry community, it has acquired some momentum over the last years.…”

Real-time GW: Toward an ab initio description of the ultrafast carrier and exciton dynamics in two-dimensional materials

“…Moreover in Ref. [38] it has been shown that second-order exchange effects are negligible. We therefore expect that 2B and GW calculations give similar results and that the comparison between GW and BE well highlights the role of non-Markovian effects.…”

Exploring the Statically Screened $G3W2$ Correction to the $GW$ Self-Energy: Charged Excitations and Total Energies of Finite Systems

“…where The structure of the self-energy terms has been scrutinized by Stefanucci, Pavlyukh, van Leeuwen and coworkers. 102,103 We follow them and use the framework of the Keldysh formalism to discuss the G3W 2 self-energy. 104 In the Keldysh formalism, we work on the contour C = C + ∪ C − , with C + being the backward branch and C − being the forward branch.…”

“…Together, the four diagrams describe three distinct scattering processes. 103,106 Among others, they are responsible for spectral features which do not appear in fully self-consistent GW , like the excitation of two plasmons and two particle hole pairs. In this work, these terms should be of minor relevance only since we are interested in improving QP energies and correlation energies.…”

“…1, however, only contributes to the 2h1p (1h2p) space and describes the exchange of two final particles/holes. 103 In the same way as the static SOX term it ensures the antisymmetry of the wave function to first order. Static screening comes with two distinct advantages.…”