Enumeration of many-body skeleton diagrams

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.

arXiv comment5 pages including 4 figures

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• Approximations for many-body Green's functions: insights from the fundamental equations
• Multiplicity of solutions to GW-type approximations
• Hypergeometric resummation of self-consistent sunset diagrams for electron-boson quantum many-body systems out of equilibrium
• Renormalized asymptotic enumeration of Feynman diagrams
• Counting Feynman diagrams via many-body relations
• Lecture notes on Diagrammatic Monte Carlo for the Fröhlich polaron
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• Grassmannization of classical models
• A recursive enumeration of connected Feynman diagrams with an arbitrary number of external legs in the fermionic non-relativistic interacting gas
• Seven Etudes on dynamical Keldysh Model
• The plain and simple parquet approximation: single- and multi-boson exchange in the two-dimensional Hubbard model