The three channels of many-body perturbation theory: $GW$, particle-particle, and electron-hole $T$-matrix self-energies

Abstract

We derive the explicit expression of the three self-energies that one encounters in many-body perturbation theory: the well-known $GW$ self-energy, as well as the particle-particle and electron-hole $T$-matrix self-energies. Each of these can be easily computed via the eigenvalues and eigenvectors of a different random-phase approximation (RPA) linear eigenvalue problem that completely defines their corresponding response function. For illustrative and comparative purposes, we report the principal ionization potentials of a set of small molecules computed at each level of theory. The performance of these schemes on strongly correlated systems (\ce{B2} and \ce{C2}) is also discussed.

13 pages, 6 figures

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• Anomalous propagators and the particle-particle channel: Hedin's equations
• Anomalous propagators and the particle-particle channel: Bethe-Salpeter equation
• Accurate and Efficient Prediction of Double Excitation Energies Using the Particle-Particle Random Phase Approximation
• Joint Approximate Diagonalization approach to Quasiparticle Self-Consistent $GW$ calculations
• Complex Absorbing Potential Green's Function Methods for Resonances
• Parquet theory for molecular systems: Formalism and static kernel parquet approximation