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.

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• Dynamical configuration interaction: Quantum embedding that combines wave functions and Green's functions
• One-electron spectra and susceptibilities of 3D electron gas from self-consistent solutions of Hedin's equations
• Vertex effects in describing the ionization energies of the first-row transition-metal monoxide molecules
• Diagrammatic approach to orbital quantum impurities interacting with a many-particle environment
• Contour calculus for many-particle functions
• Low-energy peak in the one-particle spectral function of the electron gas at metallic densities
• Cutting rules and positivity in finite temperature many-body theory
• The plain and simple parquet approximation: single- and multi-boson exchange in the two-dimensional Hubbard model