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MM: Fachverband Metall- und Materialphysik

MM 37: Development of Calculation Methods I

MM 37.1: Vortrag

Donnerstag, 12. März 2026, 15:45–16:00, SCH/A315

The two-particle Green’s function in the particle-particle channel: A survey of approximations — •Caja Annweiler¹, Lucia Reining², and Claudia Draxl¹ — ¹Humboldt Universität Berlin, Berlin, Germany — ²École Polytechnique, Palaiseau, France

While in general setting up and solving the Bethe-Salpeter equation (BSE) is out of reach for realistic systems, it provides an ideal starting point for constructing approximations. In the particle-hole channel, this has lead to established approaches such as the GW-level approximation to capture excitonic effects. This framework can be extended to the BSE in the particle-particle channel (pp-BSE), obtained by choosing a different time-ordering in the two-particle Green’s function. The result is an equation describing the propagation of two particles (either electrons or holes). While formally similar to the ph-BSE, it is a promising alternative for the calculation of the exchange-correlation energy and yields important information for topics such as pair correlations in superconductors. Despite growing interest in the pp-BSE, systematic investigations of approximations remain scarce.

In the present work we consider a variety of approximations to the pp-BSE. For this purpose, exactly solvable model systems of interacting electrons provide valuable insights into the minimal ingredients needed to capture the key physics. We present approximations from many-body perturbation theory (HF, GW, etc.) at the level of the self-energy Σ and interaction vertex Ξ on small Hubbard models, with the aim of advancing our understanding of approximations in the pp-channel.

Keywords: Many-Body Perturbation Theory; Bethe-Salpeter Equation; Interacting Electrons; Approximations