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Summing parquet diagrams using the functional renormalization group: X-ray problem revisited. (English) Zbl 1329.82081

Summary: 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 using 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.

MSC:

82C22 Interacting particle systems in time-dependent statistical mechanics
82C28 Dynamic renormalization group methods applied to problems in time-dependent statistical mechanics
81V70 Many-body theory; quantum Hall effect
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