Multiloop functional renormalization group that sums up all parquet diagrams

Abstract

We present a multiloop flow equation for the four-point vertex in the functional renormalization group (fRG) framework. The multiloop flow consists of successive one-loop calculations and sums up all parquet diagrams to arbitrary order. This provides substantial improvement of fRG computations for the four-point vertex and, consequently, the self-energy. Using the X-ray-edge singularity as an example, we show that solving the multiloop fRG flow is equivalent to solving the (first-order) parquet equations and illustrate this with numerical results.

References in corpus (9)

• Dynamical vertex approximation - a step beyond dynamical mean field theory
• Dynamical vertex approximation in its parquet implementation: application to Hubbard nano-rings
• Breakdown of traditional many-body theories for correlated electrons
• Multiloop functional renormalization group for general models
• Dual Fermion Approach to Susceptibility of Correlated Lattice Fermions
• Dynamical vertex approximation for nanoscopic systems
• Fermionic two-loop functional renormalization group for correlated fermions: Method and application to the attractive Hubbard model
• Competing instabilities, orbital ordering and splitting of band degeneracies from a parquet renormalization group analysis of a 4-pocket model for iron-based superconductors: application to FeSe
• Role of three-particle vertex within dual fermion calculations

Cited by in corpus (63)

• The nonperturbative functional renormalization group and its applications
• Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory
• Tracking the Footprints of Spin Fluctuations: A MultiMethod, MultiMessenger Study of the Two-Dimensional Hubbard Model
• Competing orders at higher-order Van Hove points
• Quantum and Classical Phases of the Pyrochlore Heisenberg Model with Competing Interactions
• Multiloop functional renormalization group for general models
• Antiferromagnetic and d-wave pairing correlations in the strongly interacting two-dimensional Hubbard model from the functional renormalization group
• Breathing chromium spinels: a showcase for a variety of pyrochlore Heisenberg Hamiltonians
• Frustrated Quantum Spins at finite Temperature: Pseudo-Majorana functional RG approach
• Analytical investigation of singularities in two-particle irreducible vertex functions of the Hubbard atom
• Quantitative functional renormalization-group description of the two-dimensional Hubbard model
• Non-separable frequency dependence of two-particle vertex in interacting fermion systems
• Multiloop functional renormalization group for the two-dimensional Hubbard model: Loop convergence of the response functions
• Multiloop functional renormalization group approach to quantum spin systems
• Derivation of exact flow equations from the self-consistent parquet relations
• Multipoint correlation functions: spectral representation and numerical evaluation
• Dual parquet scheme for the two-dimensional Hubbard model: modelling low-energy physics of high-$T_c$ cuprates with high momentum resolution
• Pseudo-fermion functional renormalization group for spin models
• Single boson exchange representation of the functional renormalization group for strongly interacting many-electron systems
• Reference results for the momentum space functional renormalization group
• Solving the Bethe-Salpeter equation with exponential convergence
• Effects of two-loop contributions in the pseudofermion functional renormalization group method for quantum spin systems
• Pseudogap opening in the two-dimensional Hubbard model: A functional renormalization group analysis
• Parametrizations of local vertex corrections from weak to strong coupling: importance of the Hedin three-leg vertex
• Fulfillment of sum rules and Ward identities in the multiloop functional renormalization group solution of the Anderson impurity model
• Multiloop flow equations for single-boson exchange fRG
• Truncated-Unity Parquet Equations: Application to the Repulsive Hubbard Model
• Deep Learning the Functional Renormalization Group
• divERGe implements various Exact Renormalization Group examples
• Functional renormalization group for fermion lattice models in three dimensions: application to the Hubbard model on the cubic lattice
• Accessing the ordered phase of correlated Fermi systems: vertex bosonization and mean-field theory within the functional renormalization group
• Taming pseudo-fermion functional renormalization for quantum spins: Finite-temperatures and the Popov-Fedotov trick
• Real-frequency quantum field theory applied to the single-impurity Anderson model
• Benchmark Calculations of Multiloop Pseudofermion fRG
• Single-boson exchange functional renormalization group application to the two-dimensional Hubbard model at weak coupling
• Counting Feynman diagrams via many-body relations
• Fermi-edge singularity and the functional renormalization group
• Holographic unitary renormalization group for correlated electrons -- II: insights on fermionic criticality
• Holographic unitary renormalization group for correlated electrons -- I: a tensor network approach
• Approximating the frequency dependence of the effective interaction in the functional renormalization group for many-fermion systems
• KeldyshQFT: A C++ codebase for real-frequency multiloop functional renormalization group and parquet computations of the single-impurity Anderson model
• Pseudo-fermion functional renormalization group with magnetic fields
• Better Integrators for Functional Renormalization Group Calculations
• Review of recent developments of the functional renormalization group for systems out of equilibrium
• Parquet approximation and one-loop renormalization group: Equivalence on the leading-logarithmic level
• Superconductivity from repulsion: Variational results for the 2D Hubbard model in the limit of weak interaction
• Finite-bias transport through the interacting resonant level model coupled to a phonon mode -- a functional renormalization group study
• Testing the parquet equations and the U(1) Ward identity for real-frequency correlation functions from the multipoint numerical renormalization group
• Subleading logarithmic behavior in the parquet formalism
• Single-boson exchange formulation of the Schwinger-Dyson equation and its application to the functional renormalization group
• Intertwined fluctuations and isotope effects in the Hubbard-Holstein model on the square lattice from functional renormalization
• The finite-difference parquet method: Enhanced electron-paramagnon scattering opens a pseudogap
• 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
• Quasi-particle functional Renormalisation Group calculations in the two-dimensional t-t'-Hubbard model
• Entanglement across scales: Quantics tensor trains as a natural framework for renormalization
• A functional-analysis derivation of the parquet equation
• Leading-logarithmic approximation by one-loop renormalization group within Matsubara formalism
• Broadening and sharpening of the Drude peak through antiferromagnetic fluctuations
• Compressing local vertex functions from the multipoint numerical renormalization group using quantics tensor cross interpolation
• Competing instabilities of the extended Hubbard model on the triangular lattice: Truncated-unity functional renormalization group and application to moiré materials
• Fluctuating local field method for the disordered Ising model
• Functional renormalization with interaction flows: A single-boson exchange perspective and application to electron-phonon systems
• The plain and simple parquet approximation: single- and multi-boson exchange in the two-dimensional Hubbard model