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

Understand

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.