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.

References in corpus (9)

• Exact evolution equation for the effective potential
• Quantum fluids of light
• Multiloop functional renormalization group that sums up all parquet diagrams
• Multiloop functional renormalization group for general models
• Renormalization group approach to interacting fermion systems in the two-particle-irreducible formalism
• Two-particle irreducible functional renormalization group schemes---a comparative study
• Fermi-edge exciton-polaritons in doped semiconductor microcavities with finite hole mass
• Light-matter interaction in doped microcavities
• Single particle polariton properties in doped quantum well microcavities: role of the Fermi edge singularity and Anderson orthogonality catastrophe

Cited by in corpus (9)

• Multiloop functional renormalization group for the two-dimensional Hubbard model: Loop convergence of the response functions
• Derivation of exact flow equations from the self-consistent parquet relations
• KeldyshQFT: A C++ codebase for real-frequency multiloop functional renormalization group and parquet computations of the single-impurity Anderson model
• Addressing energy density functionals in the language of path-integrals I: Comparative study of diagrammatic techniques applied to the (0+0)-D $O(N)$-symmetric ${\phi }^4$-theory
• Parquet approximation and one-loop renormalization group: Equivalence on the leading-logarithmic level
• Spectra of heavy polarons and molecules coupled to a Fermi sea
• Subleading logarithmic behavior in the parquet formalism
• Addressing energy density functionals in the language of path-integrals II: Comparative study of functional renormalization group techniques applied to the (0+0)-D $O(N)$-symmetric ${\phi }^4$-theory
• Leading-logarithmic approximation by one-loop renormalization group within Matsubara formalism