From models to real systems: implementation and applications of the multichannel dyson equation.- (Stefano Paggi / LPT / Thesis). -13/10/2026, 14H

PhD defense

Stefano Paggi – LPT, Salle de séminaire du 3R1, 3ème étage, 2 p.m.

Abstract :
The multichannel Dyson equation (MCDE) connects many-body Green’s functions via a multichannel many-body self-energy. Two or more many-body Green’s functions can be coupled in the MCDE. Linking one-body and three-body Green’s functions treats satellites and quasiparticles in photoemission on equal footing, whereas linking two-body and four-body Green’s functions does the same for single and double neutral excitations in optical absorption. Motivated by the exact result of the photoemission spectra of the standard Hubbard dimer, the work applies the MCDE to the extended Hubbard dimer, an H$_2$-like model, which results in an overall better estimation of the photoemission spectrum, as well as the ground state energy and the HOMO-LUMO gap compared to standard approaches like $GW$ and second Born. We also investigated neutral excitations of a two-level helium-like model using an MCDE coupling two- and four-body Green’s functions. The MCDE returns single and double neutral excitations close to the exact value, unlike standard approaches like BSE@GW. In order to apply the MCDE to real molecules, we developed an implementation in a many-body code using \python$ $ and \fortran$ $, which just needs as input parameters the restricted Hartree-Fock orbital energies, basis size, and two-electron repulsion integrals. Using a spin-adapted effective Hamiltonian and Haydock-Lanczos algorithm, the spectroscopy-specialized code is able to calculate spectra of atoms and molecules. This paves the way for the implementation of the MCDE to other spectroscopies. Currently our group is implementing the MCDE for neutral excitations, as well as double ionizations.