Summing parquet diagrams using the functional renormalization group: X-ray problem revisited

Abstract

We present a simple method for summing so-called parquet diagrams of fermionic many-body systems with competing instabilities using the functional renormalization group. Our method is based on partial bosonization of the interaction utilizing multi-channel Hubbard-Stratonovich transformations. A simple truncation of the resulting flow equations, retaining only the frequency-independent parts of the two-point and three-point vertices amounts to solving coupled Bethe-Salpeter equations for the effective interaction to leading logarithmic order. We apply our method by revisiting the X-ray problem and deriving the singular frequency dependence of the X-ray response function and the particle-particle susceptibility. Our method is quite general and should be useful in many-body problems involving strong fluctuations in several scattering channels.

Bibliography has been revised and updated 9 pages, 4 figures

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Cited by in corpus (8)

• High-frequency asymptotics of the vertex function: diagrammatic parametrization and algorithmic implementation
• Multiloop functional renormalization group that sums up all parquet diagrams
• Accessing the ordered phase of correlated Fermi systems: vertex bosonization and mean-field theory within the functional renormalization group
• Fermi-edge singularity and the functional renormalization group
• Parquet approximation and one-loop renormalization group: Equivalence on the leading-logarithmic level
• Addressing energy density functionals in the language of path-integrals I: Comparative study of diagrammatic techniques applied to the (0+0)-D $O(N)$-symmetric ${\phi }^4$-theory
• Subleading logarithmic behavior in the parquet formalism
• Leading-logarithmic approximation by one-loop renormalization group within Matsubara formalism