Divergences of the irreducible vertex functions in correlated metallic systems: Insights from the Anderson Impurity Model

Abstract

In this work, we analyze in detail the occurrence of divergences in the irreducible vertex functions for one of the fundamental models of many-body physics: the Anderson impurity model (AIM). These divergences -- a surprising hallmark of the breakdown of many-electron perturbation theory -- have been recently observed in several contexts, including the dynamical mean-field solution of the Hubbard model. The numerical calculations for the AIM presented in this work, as well as their comparison with the corresponding results for the Hubbard model, allow us to clarify several open questions about the origin and the properties of vertex divergences in a particularly interesting context, the correlated metallic regime at low-temperatures. Specifically, our analysis (i) rules out explicitly the transition to a Mott insulating phase, but not the more general suppression of charge fluctuations (proposed in [Phys.\,Rev.\,B {\bf 93},\,245102\,(2016)]), as a necessary condition for the occurrence of vertex divergences, (ii) clarifies their relation with the underlying Kondo physics, and, eventually, (iii) individuates which divergences might also appear on the real frequency axis in the limit of zero temperature, through the discovered scaling properties of the singular eigenvectors.

16 pages, 13 figures, published version

References in corpus (13)

• Hybridization expansion impurity solver: General formulation and application to Kondo lattice and two-orbital models
• Dynamical vertex approximation - a step beyond dynamical mean field theory
• Kinks in the dispersion of strongly correlated electrons
• Non-existence of the Luttinger-Ward functional and misleading convergence of skeleton diagrammatic series for Hubbard-like models
• Dynamical vertex approximation in its parquet implementation: application to Hubbard nano-rings
• Ab initio dynamical vertex approximation
• Conserved quantities of SU(2)-invariant interactions for correlated fermions and the advantages for quantum Monte Carlo simulations
• Practical consequences of Luttinger-Ward functional multivaluedness for cluster DMFT methods
• Correlated starting points for the functional renormalization group
• Efficient Bethe-Salpeter equations' treatment in dynamical mean-field theory
• Role of three-particle vertex within dual fermion calculations
• Kinks in the electronic specific heat
• Kinks in the periodic Anderson model

Cited by in corpus (57)

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• Analytical investigation of singularities in two-particle irreducible vertex functions of the Hubbard atom
• Boson-Exchange Parquet Solver for dual fermions
• 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
• Multiscale space-time ansatz for correlation functions of quantum systems based on quantics tensor trains
• Multipoint correlation functions: spectral representation and numerical evaluation
• The Bethe-Salpeter equation at the critical end-point of the Mott transition
• Parquet-like equations for the Hedin three-leg vertex
• Interplay between local response and vertex divergences in many-fermion systems with on-site attraction
• Self-consistent ladder D$\Gamma$A approach
• Efficient Bethe-Salpeter equations' treatment in dynamical mean-field theory
• Dynamical vertex approximation for the attractive Hubbard model
• Single boson exchange representation of the functional renormalization group for strongly interacting many-electron systems
• Fermion-boson vertex within Dynamical Mean-Field Theory
• Quantum criticality in the two-dimensional periodic Anderson model
• Charge-fluctuations in lightly hole-doped cuprates: effect of vertex corrections
• 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
• Luttinger's theorem in presence of Luttinger surfaces
• Fermi liquid theory and divergences of the two-particle irreducible vertex in the periodic Anderson lattice
• Two-particle Fermi liquid parameters at the Mott transition: Vertex divergences, Landau parameters, and incoherent response in dynamical mean-field theory
• Fulfillment of sum rules and Ward identities in the multiloop functional renormalization group solution of the Anderson impurity model
• Highly nonperturbative nature of the Mott metal-insulator transition: Two-particle vertex divergences in the coexistence region
• 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
• Local magnetic moment formation and Kondo screening in the half filled two dimensional single band Hubbard model
• Multi-valuedness of the Luttinger-Ward functional in the Fermionic and Bosonic System with Replicas
• Two-particle correlations and the metal-insulator transition: Iterated Perturbation Theory revisited
• Strongly correlated superconductivity with long-range spatial fluctuations
• Two-Particle Self-Consistent method for the multi-orbital Hubbard model
• Fluctuations analysis of the spin susceptibility: Néel ordering revisited in dynamical mean field theory
• Diagrammatic study of optical excitations in correlated systems
• Real-frequency quantum field theory applied to the single-impurity Anderson model
• Strongly correlated electrons: Analytic mean-field theories with two-particle self-consistency
• Single-boson exchange functional renormalization group application to the two-dimensional Hubbard model at weak coupling
• Strange Metal Solution in the Diagrammatic Theory for the $2d$ Hubbard Model
• Spectral representation of Matsubara n-point functions: Exact kernel functions and applications
• Landau-Fermi liquids without quasiparticles
• Dual Bethe-Salpeter equation for the multi-orbital lattice susceptibility within dynamical mean-field theory
• Protection of Correlation-Induced Phase Instabilities by Exceptional Susceptibilities
• Analytic continuation of multipoint correlation functions
• Compressing the two-particle Green's function using wavelets: Theory and application to the Hubbard atom
• Effective enhancement of the electron-phonon coupling driven by nonperturbative electronic density fluctuations
• Physical and unphysical regimes of self-consistent many-body perturbation theory
• Non-Perturbative Feats in the Physics of Correlated Antiferromagnets
• Single-boson exchange formulation of the Schwinger-Dyson equation and its application to the functional renormalization group
• 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
• Diagrammatic bosonization, aspects of criticality, and the Hohenberg-Mermin-Wagner theorem in parquet approaches
• Origin of misleading convergence in self-consistent many-electron theories: Fundamental aspects and practical implications
• Local magnetic moment formation and Kondo screening in the presence of Hund exchange: the two-band Hubbard model analysis
• Non-perturbative effects of short-range spatial correlations at the two-particle level