Fermi-edge singularity and the functional renormalization group
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.
Cite
@article{arxiv.1706.06872,
title = {Fermi-edge singularity and the functional renormalization group},
author = {Fabian B. Kugler and Jan von Delft},
journal= {arXiv preprint arXiv:1706.06872},
year = {2018}
}