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Multiloop functional renormalization group from single bosons

Kilian Fraboulet1,2,3,*, Aiman Al-Eryani4, Sarah Heinzelmann3, Anna Kauch5, and Sabine Andergassen2,5

  • *Contact author: k.fraboulet@fkf.mpg.de
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Phys. Rev. Research 8, 043139 – Published 6 November, 2026

DOI: https://doi.org/10.1103/k1l3-czq7

Abstract

The functional renormalization group (fRG) is an established tool in the treatment of correlated electron systems, notably for the description of competing instabilities. In recent years, methodological advancements led to the multiloop extension of the fRG, which systematically includes loop corrections beyond the conventional one-loop truncation and yields a quantitatively accurate description of two-dimensional lattice systems. At the same time, the single-boson exchange (SBE) decomposition of the two-particle vertex has been shown to offer both computational and interpretative advantages, paving the way to more affordable approximation schemes. We here apply their combination coined as multiloop SBE fRG to the two-dimensional Hubbard model at weak coupling. After providing a detailed account of the underlying formalism in physical channels, we analyze the results for the frequency- and momentum-dependent vertex functions. We find that the SBE approximation, i.e., neglecting the flow of the multiboson exchange contributions, accurately reproduces the parquet approximation at loop convergence. The presented algorithmic improvement opens the route for the treatment of more challenging parameter regimes and more realistic models.

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Phys. Rev. Research 8, 043139– Published 6 November, 2026
  • Received 1 June 2026
  • Accepted 6 October 2026
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