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.
Cite
@article{arxiv.1502.06625,
title = {Summing parquet diagrams using the functional renormalization group: X-ray problem revisited},
author = {Philipp Lange and Casper Drukier and Anand Sharma and Peter Kopietz},
journal= {arXiv preprint arXiv:1502.06625},
year = {2015}
}
Comments
Bibliography has been revised and updated 9 pages, 4 figures