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

Roberto Orlando (1, 2, 3) , Pina Romaniello (2, 3) , Pierre-François Loos (1)

1 LCPQ - Laboratoire de Chimie et Physique Quantiques
2 ETSF - European Theoretical Spectroscopy Facility
3 AGR-LPT - Agrégats (LPT)

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.

Domains: Theoretical and/or physical chemistry; Condensed Matter [cond-mat]

Roberto Orlando, Pina Romaniello, Pierre-François Loos. The three channels of many-body perturbation theory: $GW$, particle-particle, and electron-hole $T$-matrix self-energies. 2023. ⟨hal-04201951⟩