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arXiv · 1707.04536

Multiloop functional renormalization group for general models

Fabian B. Kugler·Jan von Delft
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Abstract

We present multiloop flow equations in the functional renormalization group (fRG) framework for the four-point vertex and self-energy, formulated for a general fermionic many-body problem. This generalizes the previously introduced vertex flow [F. B. Kugler and J. von Delft, Phys. Rev. Lett. 120, 057403 (2018)] and provides the necessary corrections to the self-energy flow in order to complete the derivative of all diagrams involved in the truncated fRG flow. Due to its iterative one-loop structure, the multiloop flow is well-suited for numerical algorithms, enabling improvement of many fRG computations. We demonstrate its equivalence to a solution of the (first-order) parquet equations in conjunction with the Schwinger-Dyson equation for the self-energy.

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Fabian B. Kugler, Jan von Delft. 2018-02-14. Multiloop functional renormalization group for general models. https://doi.org/10.1103/physrevb.97.035162

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