Vertex corrections for positive-definite spectral functions of simple metals

TL;DR

This paper systematically investigates vertex corrections in the spectral functions of simple metals, revealing new physical processes and explaining experimental observations through a positive-definite diagrammatic approach.

Contribution

It introduces a positive-definite diagrammatic expansion for spectral functions, enabling detailed analysis of vertex corrections and their physical implications in simple metals.

Findings

Vertex corrections lead to bandwidth reduction in sodium.

Secondary plasmon satellites are explained by new scattering channels.

Spectral weight redistribution matches experimental photoemission data.

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.