Enumeration of many-body skeleton diagrams

TL;DR

This paper systematically counts dressed Feynman (skeleton) diagrams derived from Hedin's equations in zero-dimensional space-time, providing foundational checks for future many-body theory extensions.

Contribution

It introduces a method to enumerate skeleton diagrams based on Hedin's equations, aiding the validation of advanced many-body computational approaches.

Findings

Counts of skeleton diagrams are explicitly derived.

Provides a basis for verifying future many-body simulations.

Enhances understanding of diagrammatic complexity in many-body physics.

Abstract

The many-body dynamics of interacting electrons in condensed matter and quantum chemistry is often studied at the quasiparticle level, where the perturbative diagrammatic series is partially resummed. Based on Hedin's equations for self-energy, polarization, propagator, effective potential, and vertex function in zero dimension of space-time, dressed Feynman (skeleton) diagrams are enumerated. Such diagram counts provide useful basic checks for extensions of the theory for future realistic simulations.