Vertex Corrections for Positive-Definite Spectral Functions of Simple Metals

Abstract

We present a systematic study of vertex corrections in the homogeneous electron gas at metallic densities. The vertex diagrams are built using a recently proposed positive-definite diagrammatic expansion for the spectral function. The vertex function not only provides corrections to the well known plasmon and particle-hole scatterings, but also gives rise to new physical processes such as generation of two plasmon excitations or the decay of the one-particle state into a two-particles-one-hole state. By an efficient Monte Carlo momentum integration we are able to show that the additional scattering channels are responsible for the bandwidth reduction observed in photoemission experiments on bulk sodium, appearance of the secondary plasmon satellite below the Fermi level, and a substantial redistribution of spectral weights. The feasibility of the approach for first-principles band-structure calculations is also discussed.

Padé resummation of many-body perturbation theories

“…Our analysis (Fig. 6) thus justifies the use of GW approximation for the monolayer graphene 47, 48 . Similar conclusion holds for fullerenes ( r s  ≈ 1.0), which are molecules of graphene wrapped by the introduction of pentagons on the hexagonal lattice, endorsing the use of GW for these systems 49, 50 .…”

“…The six-dimensional integration in M (2) can be somewhat simplified in spherical coordinates and reduced so to a 4d integral amenable to the Monte-Carlo approach introduced in ref. 47 and applied in refs 45, 46 and 48 to more complicated problems. Nonetheless it is instructive to introduce an approximation with the goal of estimating the a -parameter analytically.…”

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

“…Whether this overestimation comes from the inaccuracy of analytical continuation or from intrinsic insufficiencies of the schemes is diffucult to conclude at this point. Plasmon satellites in electron gas have been studied recently using the positive-definite diagrammatic expansion for the spectral function 14 and the GW+Cumulant approach. [33][34][35][36] Both methods are implemented on real frequency axis and, thus, do not involve analytical continuation as an intermediate step in evaluating the spectral function.…”

Diagrammatic approach to orbital quantum impurities interacting with a many-particle environment

“…These regions always appear near the phonon branch, and originate in omission of some of the higher-order diagrams, which does not affect the quasiparticle peaks lying at lower energies. This problem has been known for a long time in the case of an electron gas [115,116] and has found a solutionapplicable in all generality to any many-body diagrammatic expansion -only recently [117,118]. In particular, it has been demonstrated that, in general, the n-th order truncation of a diagrammatic expansion does not lead to a positive-definite spectral function, whereas an opportune combination of all diagrams up to the n-th order plus certain (n + 1)-th order diagrams is positivedefinite.…”

“…Following the approach in Refs. [117,118] one can divide each one of the second-order diagrams in two half-diagrams [118]. Then a minimal, positive-definite set of diagrams can be found by 'completing the square', i.e.…”