Summing parquet diagrams using the functional renormalization group: X-ray problem revisited

Abstract

We present a simple method for summing so-called parquet diagrams of fermionic many-body systems with competing instabilities using the functional renormalization group. Our method is based on partial bosonization of the interaction utilizing multi-channel Hubbard-Stratonovich transformations. A simple truncation of the resulting flow equations, retaining only the frequency-independent parts of the two-point and three-point vertices amounts to solving coupled Bethe-Salpeter equations for the effective interaction to leading logarithmic order. We apply our method by revisiting the X-ray problem and deriving the singular frequency dependence of the X-ray response function and the particle-particle susceptibility. Our method is quite general and should be useful in many-body problems involving strong fluctuations in several scattering channels.

arXiv commentBibliography has been revised and updated 9 pages, 4 figures

References in corpus (28)

• Exact evolution equation for the effective potential
• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• Renormalization Group Approach to Interacting Fermions
• Bosonization and Strongly Correlated Systems
• Aspects of the Functional Renormalisation Group
• Optimised Renormalisation Group Flows
• Functional renormalization group approach to correlated fermion systems
• Magnetism, superconductivity, and pairing symmetry in Fe-based superconductors
• Nonanalytic behavior of the spin susceptibility in clean Fermi systems
• Efficient Parametrization of the Vertex Function, $\Omega$-Scheme, and the (t,t')-Hubbard Model at Van Hove Filling
• Parquet solution for a flat Fermi surface
• Nonequilibrium functional RG with frequency dependent vertex function: A study of the single impurity Anderson model
• A finite-frequency functional RG approach to the single impurity Anderson model
• Superconductivity from weak repulsion in hexagonal lattice systems
• Effects of the Van Hove singularities on magnetism and superconductivity in the t-t' Hubbard model: a parquet approach
• Renormalization group flow, competing phases, and the structure of superconducting gap in multi-band models of Iron based superconductors
• Functional renormalization group approach to zero-dimensional interacting systems
• Collective fields in the functional renormalization group for fermions, Ward identities, and the exact solution of the Tomonaga-Luttinger model
• Self-energy flows in the two-dimensional repulsive Hubbard model
• Solving the Parquet Equations for the Hubbard Model beyond Weak Coupling
• Frequency Dependent Vertex Functions of the (t,t')-Hubbard Model at Weak Coupling
• Stability of self-consistent solutions for the Hubbard model at intermediate and strong coupling
• Exact renormalization group flow equations for non-relativistic fermions: scaling towards the Fermi surface
• Analytic impurity solver with the Kondo strong-coupling asymptotics
• Functional Renormalization Group Approach for Inhomogeneous Interacting Fermi-Systems
• Parquet Graph Resummation Method for Vortex Liquids
• Summation of Parquet diagrams as an ab initio method in nuclear structure calculations
• Non-analytic magnetic field dependence of quasi-particle properties of two-dimensional metals

Cited by in corpus (8)

• High-frequency asymptotics of the vertex function: diagrammatic parametrization and algorithmic implementation
• Multiloop functional renormalization group that sums up all parquet diagrams
• Accessing the ordered phase of correlated Fermi systems: vertex bosonization and mean-field theory within the functional renormalization group
• Fermi-edge singularity and the functional renormalization group
• Parquet approximation and one-loop renormalization group: Equivalence on the leading-logarithmic level
• 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
• Subleading logarithmic behavior in the parquet formalism
• Leading-logarithmic approximation by one-loop renormalization group within Matsubara formalism