Multiloop flow equations for single-boson exchange fRG

Marcel Gievers, Elias Walter, Anxiang Ge, Jan von Delft and Fabian B. Kugler ()
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Marcel Gievers: Ludwig-Maximilians-Universität München
Elias Walter: Ludwig-Maximilians-Universität München
Anxiang Ge: Ludwig-Maximilians-Universität München
Jan von Delft: Ludwig-Maximilians-Universität München
Fabian B. Kugler: Rutgers University

The European Physical Journal B: Condensed Matter and Complex Systems, 2022, vol. 95, issue 7, 1-22

Abstract: Abstract The recently introduced single-boson exchange (SBE) decomposition of the four-point vertex of interacting fermionic many-body systems is a conceptually and computationally appealing parametrization of the vertex. It relies on the notion of reducibility of vertex diagrams with respect to the bare interaction U, instead of a classification based on two-particle reducibility within the widely used parquet decomposition. Here, we re-derive the SBE decomposition in a generalized framework (suitable for extensions to, e.g., inhomogeneous systems or real-frequency treatments) following from the parquet equations. We then derive multiloop functional renormalization group (mfRG) flow equations for the ingredients of this SBE decomposition, both in the parquet approximation, where the fully two-particle irreducible vertex is treated as an input, and in the more restrictive SBE approximation, where this role is taken by the fully U-irreducible vertex. Moreover, we give mfRG flow equations for the popular parametrization of the vertex in terms of asymptotic classes of the two-particle reducible vertices. Since the parquet and SBE decompositions are closely related, their mfRG flow equations are very similar in structure. Graphic abstract

Date: 2022
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Citations: View citations in EconPapers (2)

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DOI: 10.1140/epjb/s10051-022-00353-6

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