One-electron spectra and susceptibilities of the three-dimensional electron gas from self-consistent solutions of Hedin's equations

Abstract

A few approximate schemes to solve the Hedin equations 1 self-consistently introduced in (Phys. Rev. B 94, 155101 (2016)) are explored and tested for the 3D electron gas at metallic densities. We calculate one electron spectra, dielectric properties, compressibility, and correlation energy. Considerable reduction in the calculated band width (as compared to the self consistent GW result) has been found when vertex correction was used for both polarizability and self energy. Generally, it is advantageous to obtain the diagrammatic representation of polarizability from the definition of this quantity as a functional derivative of the electronic density with respect to the total field (external plus induced). For self energy, the first order vertex correction seems to be sufficient for the range of densities considered. Whenever it is possible, we compare the accuracy of our vertex-corrected schemes with the accuracy of the self-consistent quasi-particle GW approximation (QSGW), which is less expensive computationally. We show that QSGW approach performs poorly and we relate this poor performance with an inaccurate description of the screening in the QSGW method (with an error comprising a factor 2-3 in the physically important range of momenta).

A combined variational and diagrammatic quantum Monte Carlo approach to the many-electron problem

“…We want to point out that finite temperature calculations are very hard in the Diffusion Monte Carlo (DMC) 27 , while our method is very well suited for finite temperature calculations, and converges even faster with the increasing order. While wave function properties, such as energy and pair distribution function, are very precisely computed by DMC 27 , and some of them are also are amenable to approximations such as GW 28,29 , the response functions are more challenging to evaluate with the existing techniques. The strength of our approach is that it can be used to compute both the static and the dynamic, the single and the multiparticle correlation functions.…”

Ground state properties of 3d metals from self-consistent GW approach

“…[38]) and in scGW (scheme A) approximation as a function of r s (radius of the sphere containing one electron). The data have been taken from our work on the electron gas [39].…”

Dynamically screened vertex correction to GW

“…The effect of the vertex function in Ref. [78] is rather small, therefore, it would be interesting if these calculations could be extended towards larger r s , where even variational and backflow reptation MC results are in disagreement.…”

“…In their method, the self-energy is in the GW form, however, the screened interaction is replaced by the Kukkonen-Overhauser effective interaction [77]. Furthermore, a diagrammatic approach based on the Bethe-Salpeter equation for the improved screened interaction by Kutepov and Kotliar [78] is also used for comparison. Unfortunately, none of these theories are available for graphene systems.…”

“…GW is a scheme D of Ref. [78], it includes the first-order vertex function in the finite temperature formalism. For BLG, † Ref.…”