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  • Open Access

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

Patrick Kappl, Tin Ribic, Anna Kauch*, and Karsten Held

  • Institute of Solid State Physics, TU Wien, 1040 Vienna, Austria

  • *Contact author: kauch@ifp.tuwien.ac.at
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Phys. Rev. Research 7, 043033 – Published 8 October, 2025

DOI: https://doi.org/10.1103/fqmb-h9lb

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 then only qualitatively—at least for the nonlinear response function analyzed.

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Phys. Rev. Research 7, 043033– Published 8 October, 2025
  • Received 28 November 2024
  • Accepted 10 September 2025
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