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