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arXiv · 1706.06872

Fermi-edge singularity and the functional renormalization group

Fabian B. Kugler·Jan von Delft
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Abstract

We study the Fermi-edge singularity, describing the response of a degenerate electron system to optical excitation, in the framework of the functional renormalization group (fRG). Results for the (interband) particle-hole susceptibility from various implementations of fRG (one- and two- particle-irreducible, multi-channel Hubbard-Stratonovich, flowing susceptibility) are compared to the summation of all leading logarithmic (log) diagrams, achieved by a (first-order) solution of the parquet equations. For the (zero-dimensional) special case of the X-ray-edge singularity, we show that the leading log formula can be analytically reproduced in a consistent way from a truncated, one-loop fRG flow. However, reviewing the underlying diagrammatic structure, we show that this derivation relies on fortuitous partial cancellations special to the form of and accuracy applied to the X-ray-edge singularity and does not generalize.

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Fabian B. Kugler, Jan von Delft. 2017-06-21. Fermi-edge singularity and the functional renormalization group. https://doi.org/10.1088/1361-648x%2Faaba2e

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