Single-boson exchange decomposition of the vertex function

Abstract

We present a decomposition of the two-particle vertex function of the single-band Anderson impurity model which imparts a physical interpretation of the vertex in terms of the exchange of bosons of three flavors. We evaluate the various components of the vertex for an impurity model corresponding to the half-filled Hubbard model within dynamical mean-field theory. For small values of the interaction almost the entire information encoded in the vertex function corresponds to single-boson exchange processes, which can be represented in terms of the Hedin three-leg vertex and the screened interaction. Also for larger interaction, the single-boson exchange still captures scatterings between electrons and the dominant low-energy fluctuations and provides a unified description of the vertex asymptotics. The proposed decomposition of the vertex does not require the matrix inversion of the Bethe-Salpeter equation. Therefore, it represents a computationally lighter and hence more practical alternative to the parquet decomposition.

arXiv comment11 pages main text (17 total), 13 figures

References in corpus (50)

• Continuous-time Monte Carlo methods for quantum impurity models
• The ALPS project release 2.0: Open source software for strongly correlated systems
• Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory
• Dynamical vertex approximation - a step beyond dynamical mean field theory
• Local Electronic Correlation at the Two-Particle Level
• Kinks in the dispersion of strongly correlated electrons
• Efficient Parametrization of the Vertex Function, $\Omega$-Scheme, and the (t,t')-Hubbard Model at Van Hove Filling
• w2dynamics: Local one- and two-particle quantities from dynamical mean field theory
• Non-existence of the Luttinger-Ward functional and misleading convergence of skeleton diagrammatic series for Hubbard-like models
• Fluctuation diagnostics of the electron self-energy: Origin of the pseudogap physics
• Dual boson approach to collective excitations in correlated fermionic systems
• Controlling Feynman diagrammatic expansions: physical nature of the pseudo gap in the two-dimensional Hubbard model
• Divergent Precursors of the Mott-Hubbard Transition at the Two-Particle Level
• Improved Estimators for the Self-Energy and Vertex Function in Hybridization Expansion Continuous-Time Quantum Monte Carlo Simulations
• A finite-frequency functional RG approach to the single impurity Anderson model
• Breakdown of traditional many-body theories for correlated electrons
• Dynamical vertex approximation in its parquet implementation: application to Hubbard nano-rings
• Efficient implementation of the parquet equations -- role of the reducible vertex function and its kernel approximation
• Non-perturbative landscape of the Mott-Hubbard transition: Multiple divergence lines around the critical endpoint
• Efficient treatment of two-particle vertices in dynamical mean-field theory
• Impact of nonlocal correlations over different energy scales: A Dynamical Vertex Approximation study
• Divergences of the irreducible vertex functions in correlated metallic systems: Insights from the Anderson Impurity Model
• Parquet decomposition calculations of the electronic self-energy
• Practical consequences of Luttinger-Ward functional multivaluedness for cluster DMFT methods
• Analytical investigation of singularities in two-particle irreducible vertex functions of the Hubbard atom
• Fluctuoscopy of Disordered Two-Dimensional Superconductors
• Worm Improved Estimators in Continuous-time Quantum Monte Carlo
• Collective Modes in Excitonic Magnets: Dynamical Mean-Field Study
• Effective Heisenberg model and exchange interaction for strongly correlated systems
• Parquet-like equations for the Hedin three-leg vertex
• From local to non-local correlations: the Dual Boson perspective
• Continuous-time quantum Monte Carlo calculation of multi-orbital vertex asymptotics
• Efficient Bethe-Salpeter equations' treatment in dynamical mean-field theory
• Thermodynamically consistent description of criticality in models of correlated electrons
• Symmetric Improved Estimators for Continuous-time Quantum Monte Carlo
• Fermion-boson vertex within Dynamical Mean-Field Theory
• Efficient evaluation of the polarization function in dynamical mean-field theory
• Charge-fluctuations in lightly hole-doped cuprates: effect of vertex corrections
• $p$-orbital density wave with $d$ symmetry in high-$T_c$ cuprate superconductors predicted by the renormalization-group + constrained RPA theory
• Four-point vertex in the Hubbard model and partial bosonization
• Two-particle Fermi liquid parameters at the Mott transition: Vertex divergences, Landau parameters, and incoherent response in dynamical mean-field theory
• Realistic theory of electronic correlations in nanoscopic systems
• Kondo behavior in the asymmetric Anderson model: Analytic approach
• Truncated-Unity Parquet Equations: Application to the Repulsive Hubbard Model
• Parquet approximation for molecules: spectrum and optical conductivity of the Pariser-Parr-Pople model
• Functional renormalization group for d-wave superconductivity in Hubbard type models
• Magnetic Properties of the t-J Model in the Dynamical Mean-Field Theory
• Complementary views on electron spectra: From Fluctuation Diagnostics to real space correlations
• Hedin Equations, GW, GW+DMFT, and All That
• Superconducting fluctuation corrections to ultrasound attenuation in layered superconductors

Cited by in corpus (44)

• High-frequency asymptotics of the vertex function: diagrammatic parametrization and algorithmic implementation
• Fingerprints of the local moment formation and its Kondo screening in the generalized susceptibilities of many-electron problems
• Attractive effect of a strong electronic repulsion -- the physics of vertex divergences
• Boson-Exchange Parquet Solver for dual fermions
• Impact of partially bosonized collective fluctuations on electronic degrees of freedom
• Parquet-like equations for the Hedin three-leg vertex
• Fluctuation diagnostic of the nodal/antinodal dichotomy in the Hubbard model at weak coupling: a parquet dual fermion approach
• Interplay between local response and vertex divergences in many-fermion systems with on-site attraction
• Tiling with triangles: parquet and $GW\gamma$ methods unified
• Explaining the pseudogap through damping and antidamping on the Fermi surface by imaginary spin scattering
• Single boson exchange representation of the functional renormalization group for strongly interacting many-electron systems
• How to read between the lines of electronic spectra: the diagnostics of fluctuations in strongly correlated electron systems
• Solving the Bethe-Salpeter equation with exponential convergence
• Fermi liquid theory and divergences of the two-particle irreducible vertex in the periodic Anderson lattice
• Parametrizations of local vertex corrections from weak to strong coupling: importance of the Hedin three-leg vertex
• Multiloop flow equations for single-boson exchange fRG
• The dynamical vertex approximation for many-electron systems with spontaneously broken SU(2)-symmetry
• Non-perturbative intertwining between spin and charge correlations: A "smoking gun" single-boson-exchange result
• Two-particle correlations and the metal-insulator transition: Iterated Perturbation Theory revisited
• Partial bosonisation for the two-dimensional Hubbard model: How well does it work?
• Strongly correlated superconductivity with long-range spatial fluctuations
• Accessing the ordered phase of correlated Fermi systems: vertex bosonization and mean-field theory within the functional renormalization group
• Fluctuations analysis of the spin susceptibility: Néel ordering revisited in dynamical mean field theory
• Real-frequency quantum field theory applied to the single-impurity Anderson model
• Single-boson exchange functional renormalization group application to the two-dimensional Hubbard model at weak coupling
• Spectral representation of Matsubara n-point functions: Exact kernel functions and applications
• Symmetric improved estimators for multipoint vertex functions
• KeldyshQFT: A C++ codebase for real-frequency multiloop functional renormalization group and parquet computations of the single-impurity Anderson model
• General Shiba mapping for on-site four-point correlation functions
• Analytic continuation of multipoint correlation functions
• Unambiguous fluctuation decomposition of the self-energy: pseudogap physics beyond spin fluctuations
• Testing the parquet equations and the U(1) Ward identity for real-frequency correlation functions from the multipoint numerical renormalization group
• MatsubaraFunctions.jl: An equilibrium Green's function library in the Julia programming language
• Single-boson exchange formulation of the Schwinger-Dyson equation and its application to the functional renormalization group
• Pairing boost from enhanced spin-fermion coupling in the pseudogap regime
• Subleading logarithmic behavior in the parquet formalism
• 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
• Suppression of the charge fluctuations by nonlocal correlations close to the Mott transition
• 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
• Diagrammatic bosonization, aspects of criticality, and the Hohenberg-Mermin-Wagner theorem in parquet approaches
• Functional renormalization with interaction flows: A single-boson exchange perspective and application to electron-phonon systems
• Non-perturbative effects of short-range spatial correlations at the two-particle level
• The plain and simple parquet approximation: single- and multi-boson exchange in the two-dimensional Hubbard model