Lange, Philipp; Drukier, Casper; Sharma, Anand; Kopietz, Peter Summing parquet diagrams using the functional renormalization group: X-ray problem revisited. (English) Zbl 1329.82081 J. Phys. A, Math. Theor. 48, No. 39, Article ID 395001, 16 p. (2015). 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 Keywords:functional renormalization group; parquet; X-ray problem PDFBibTeX XMLCite \textit{P. Lange} et al., J. Phys. A, Math. Theor. 48, No. 39, Article ID 395001, 16 p. (2015; Zbl 1329.82081) Full Text: DOI arXiv