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In structural analysis, singularity functions are crucial in simplifying the representation of shear forces in beams under discontinuous loading. These functions describe discontinuous  variations in shear force across a beam with varying loads by using a single mathematical expression, regardless of the complexity of the loading conditions. The singularity functions are derived from creating a free-body diagram of the beam and then making conceptual cuts at specific points to examine the...
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Fermi-edge singularity and the functional renormalization group.

Fabian B Kugler1, Jan von Delft1

  • 1Physics Department, Arnold Sommerfeld Center for Theoretical Physics, and Center for NanoScience, Ludwig-Maximilians-Universität München, Theresienstr. 37, 80333 Munich, Germany.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|March 29, 2018
PubMed
Summary
This summary is machine-generated.

We investigated the Fermi-edge singularity using functional renormalization group (fRG) methods. While fRG can reproduce specific results for the x-ray-edge singularity, this success does not generalize to broader applications.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Many-Body Theory
  • Strongly Correlated Electron Systems

Background:

  • The Fermi-edge singularity describes the optical excitation response of degenerate electron systems.
  • Understanding these singularities is crucial for characterizing electronic properties in materials.

Purpose of the Study:

  • To study the Fermi-edge singularity within the functional renormalization group (fRG) framework.
  • To compare different fRG implementations with diagrammatic techniques like parquet equations.
  • To assess the generalizability of fRG methods for describing such phenomena.

Main Methods:

  • Application of various functional renormalization group (fRG) implementations: one- and two-particle-irreducible, multi-channel Hubbard-Stratonovich, and flowing susceptibility.
  • Comparison of fRG results with the summation of leading logarithmic diagrams obtained from parquet equations.
  • Analytical investigation of the x-ray-edge singularity as a special case.

Main Results:

  • Different fRG implementations yield results for the particle-hole susceptibility.
  • A truncated one-loop fRG flow analytically reproduces the leading logarithmic formula for the x-ray-edge singularity.
  • This reproduction relies on specific cancellations and does not represent a general capability of the method.

Conclusions:

  • The success of fRG in reproducing the x-ray-edge singularity is case-specific.
  • The underlying diagrammatic structure reveals limitations for generalizing this approach.
  • Further development is needed for fRG to reliably describe broader Fermi-edge singularity phenomena.