Beyond the GW method in theoretical electron spectroscopy

The GW approximation to the self-energy of many-body perturbation theory (MBPT) is a widespread tool for the prediction of electronic excitations in materials and chemical compounds. It has been particularly effective for the calculation of band gaps of extended systems, and has recently been shown to well describe binding energies of electrons in molecules at large, even down to core levels. However, GW does not come without its own share of limitations: self-consistency (or lack thereof), prediction of photoemission satellites and description of strong correlations are all known issues of GW.

In this seminar I will review the fundamentals of the GW approximation, point out what the theory misses, and present vertex corrections as a systematic way to go beyond GW. Both low-order (second Born, GW plus second-order screened exchange)1 and high-order (time-dependent Hartree-Fock) self-energies2, 3 will be considered, as generated by a vertex correction. A numerical benchmark of these self-energies will be presented, which was performed using a test set of spherical atoms. With the support of numerical evidence, I will assess the performance of the various approximations to the self-energy, discuss the issue of choosing a starting point within and beyond GW, and introduce possible developments for describing photoemission satellites of finite systems.

References:
[1] S. Vacondio, D. Varsano, A. Ruini, A. Ferretti, Numerically Precise Benchmark of Many-Body Self-Energies on Spherical Atoms, J. Chem. Theory Comput.  18, 3703 (2022).
[2] S. Vacondio, D. Varsano, A. Ruini, A. Ferretti, Beyond GW with the time-dependent Hartree-Fock vertex, preprint (2023).
[3] S. Vacondio, PhD Thesis, Università degli Studi di Modena e Reggio Emilia (2023) Avaiable: https://hdl.handle.net/11380/1327127.

Seminar realized in the framework of the funded project:
MAX- Materials design at the Exascale - GA No. 101093374