Leading-logarithmic approximation by one-loop renormalization group within Matsubara formalism

Physical review. B./Physical review. B, vol. 109

Abstract

We demonstrate how to devise a Matsubara-formalism-based one-loop approximation to the flow of the functional renormalization group (FRG) that reproduces identically the leading-logarithmic parquet approximation. This construction of a controlled fermionic FRG approximation in a regime not accessible by perturbation theory generalizes a previous study from the real-time zero-temperature formalism to the Matsubara formalism and thus to the de facto standard framework used for condensed-matter FRG studies. Our investigation is based on a simple model for the absorption of x rays in metals. It is a core part of our construction to exploit that in a suitable leading-logarithmic approximation the values of the particle-hole susceptibility on the real- and on the imaginary-frequency axes are identical.

Authors 2

1. Jan Diekmann Aachen Institut für Theorie der Statistischen Physik

   RWTH Aachen University

   Affiliation as printed

   Institut für Theorie der Statistischen Physik, RWTH Aachen University, 52056 Aachen, Germany and JARA–Fundamentals of Future Information Technology, 52056 Aachen, Germany

2. Severin G. Jakobs Aachen Institut für Theorie der Statistischen Physik

   RWTH Aachen University

   Affiliation as printed

   Institut für Theorie der Statistischen Physik, RWTH Aachen University, 52056 Aachen, Germany and JARA–Fundamentals of Future Information Technology, 52056 Aachen, Germany