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arXiv · 2412.01848

Ladder equation for the three-particle vertex and its approximate solution

Patrick Kappl·Tin Ribic·Anna Kauch·Karsten Held
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Abstract

We generalize the three two-particle Bethe-Salpeter equations to ten three-particle ladders. These equations are exact and yield the exact three-particle vertex, if we knew the three-particle vertex irreducible in one of the ten channels. However, as we do not have this three-particle irreducible vertex at hand, we approximate this building block for the ladder by the sum of two-particle irreducible vertices each connecting two fermionic lines. The comparison to the exact solution shows that this approximation is only good for rather weak interactions and even than only qualitatively - at least for the non-linear response function analyzed.

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Patrick Kappl, Tin Ribic, Anna Kauch, Karsten Held. 2024-11-27. Ladder equation for the three-particle vertex and its approximate solution. https://arxiv.org/abs/2412.01848

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