Parquet approximation and one-loop renormalization group: Equivalence on the leading-logarithmic level

Abstract

We investigate the functional renormalization group (FRG) flow of the two-particle vertex function of a model for X-ray absorption in metals. Concerning the appearance of logarithmic divergences, the model is prototypical for an important class of mostly zero- and one-dimensional systems which includes the Kondo model and the interacting one-dimensional Fermi gas. For our analysis we formulate the FRG in the framework of the real-time zero-temperature formalism, in which the model was studied before with a parquet-based approach. We establish that a reasonably crafted, purely-fermionic one-loop FRG approximation is fully equivalent on a detailed level to the leading-logarithmic parquet approximation. These two approximation schemes are thus found to just represent different perspectives on the same technical steps. This finding also reconfirms the traditional understanding of the capabilities of one-loop RG approximations for such models, which was recently put into question by an investigation of the X-ray-absorption model with multiloop FRG.

22 pages, 6 figures, version essentially as published

References in corpus (4)

• Dynamical vertex approximation - a step beyond dynamical mean field theory
• A finite-frequency functional RG approach to the single impurity Anderson model
• The two-loop functional renormalization-group approach to the one- and two-dimensional Hubbard model
• Kondo model in nonequilibrium: Interplay between voltage, temperature, and crossover from weak to strong coupling

Cited by in corpus (5)

• Fulfillment of sum rules and Ward identities in the multiloop functional renormalization group solution of the Anderson impurity model
• Multiloop flow equations for single-boson exchange fRG
• Finite-bias transport through the interacting resonant level model coupled to a phonon mode -- a functional renormalization group study
• Subleading logarithmic behavior in the parquet formalism
• Leading-logarithmic approximation by one-loop renormalization group within Matsubara formalism