Regensburg 2019 – scientific programme

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TT: Fachverband Tiefe Temperaturen

TT 44: Correlated Electrons: Method Development

TT 44.3: Talk

Wednesday, April 3, 2019, 15:30–15:45, H7

Leading logarithmic approximation to the X-ray-edge model from a single-loop functional renormalization group approach — •Jan Diekmann and Severin Georg Jakobs — Institut für Theorie der Statistischen Physik, RWTH Aachen University, 52056 Aachen

Numerous models for low-dimensional correlated systems (e.g. X-ray-edge model, Kondo model, one-dimensional metals) have logarithmic divergencies in different diagrammatic channels of the four-point function. Then the sum of all parquet diagrams with bare lines contains all leading logarithmic divergencies, cf. Ref. [1]. The functional renormalization group (FRG) in a single-loop truncation does not reproduce all parts of all parquet diagrams; recently, it was shown how a multi-loop extension of the FRG can achieve this [2]. However, in this talk we present a (purely Fermionic) single-loop FRG that reproduces identically the leading logarithmic result of Ref. [1] for the four-point function of the X-ray-edge model. Our FRG approximation accounts for the leading contribution of every parquet diagram and is closely related to the parquet approach of Ref. [1]. Indeed, certain technical steps in Ref. [1] can be understood as introducing an RG cut-off and solving the very single-loop FRG flow equation. We expect that our findings can be transferred to other models with logarithmic divergencies.
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