Condensed Matter Seminar: Multiloop functional renormalization group that sums up all parquet diagrams

Fabian Kugler (LMU)
The functional renormalization group (fRG) is a versatile, quantum-field-theoretical formulation of the powerful RG idea and has seen a large number of successful applications.

Fabian Kugler (LMU)
Online Seminar
Mon 20. July 2020, 11:30 am (MEZ)

Abstract:

The functional renormalization group (fRG) is a versatile, quantum-field-theoretical formulation of the powerful RG idea and has seen a large number of successful applications. The main limitation of this framework is the truncation of the hierarchy of flow equations, where effective three-particle interactions are typically neglected altogether. Here, we first present multiloop fRG flow equations [1,2] as a way of simulating all contributions of the six-point vertex that can be kept efficiently. The resulting flow consists of successive one-loop calculations and sums up a complete class of diagrams. This restores the independence of the results from the choice of regulator and enables improvement of many fRG computations. Second, we show how to derive the multiloop flow equations from the self-consistent parquet relations on an algebraic basis [3]. We illustrate our approach with diagrams and numerical results of the Xray-edge singularity [1] and mention further applications to impurity and Hubbard models as well as quantum magnets.

References

[1] F. B. Kugler and J. von Delft, PRL 120, 057403 (2018)
[2] F. B. Kugler and J. von Delft, PRB 97, 035162 (2018)
[3] F. B. Kugler and J. von Delft, New J. Phys. 20, 123029 (2018)