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O: Fachverband Oberflächenphysik

O 82: Electronic Structure Theory I

O 82.8: Vortrag

Donnerstag, 21. März 2024, 12:15–12:30, MA 043

Total energies from the Klein and the Luttinger-Ward functionals: analytical benchmarking of conserving many-body approximations — •Giovanna Lani¹ and Nicola Marzari^1,2 — ¹École Polytechnique Fédérale de Lausanne, Lausanne — ²Laboratory for Materials Simulations, Paul Scherrer Institute, Villigen, Switzerland

We investigate analytically the performance of two many-body energy functionals, derived respectively by Klein and Luttinger and Ward, at different levels of diagrammatic approximations (2B, GW and T-matrix), for the calculation of total energies. We benchmark our results on the extended two-site Hubbard model, which is analytically solvable and for which several exact properties can be calculated. Despite its simplicity, this model is prototypical of the H₂ dissociation, a notoriously difficult problem to tackle for most mean-field based approaches. We show that both functionals exhibit good to excellent variational properties, particularly in the case of the Luttinger-Ward one, which is in close agreement with fully self-consistent calculations, and we elucidate the relation between the accuracy of the results and the different input one-body Green’s functions. Provided that such input is wisely chosen, we demonstrate how the Luttinger-Ward functional can be used as a computationally less expensive alternative to fully self-consistent many-body calculations, without sacrificing the precision of the results. In virtue of this accuracy, we argue that this functional can also be used to rank many-body approximations at different regimes of electronic correlation, thus bypassing the need for self-consistency.

Keywords: Total energies calculations; Many-body perturbation theory; Density-Functional theory; GW approximation; Hubbard model