Interplay between local response and vertex divergences in many-fermion systems with on-site attraction

Abstract

We investigate the divergences appearing in the two-particle irreducible vertex functions of many-fermion systems with attractive on-site interactions. By means of dynamical mean-field theory calculations, we determine the location of singularity lines in the phase diagram of the attractive Hubbard model at half-filling, where the local Bethe-Salpeter equations are non invertible. We find that divergences appear both in the magnetic and in the density scattering channels. The former affect a sector of suppressed fluctuations and comply with the mapping of the physical susceptibilities of the repulsive case. At the same time, the appearance of singularities in the density channel of the attractive model demonstrates that vertex divergences can also plague the dominant scattering sectors associated with enhanced local susceptibilities. This constitutes a counterexample to previously proposed interpretations. Eventually, by exploiting the underlying physical symmetries and a spectral representation of the susceptibilities, we clarify the relation between vertex divergences and the local response of the system in different channels.

References in corpus (49)

• Continuous-time Monte Carlo methods for quantum impurity models
• Quantum Cluster Theories
• Functional renormalization group approach to correlated fermion systems
• Dynamical phase transition in correlated fermionic lattice systems
• Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory
• Dynamical vertex approximation - a step beyond dynamical mean field theory
• Exact solution of the Falicov-Kimball model with dynamical mean-field theory
• Local Electronic Correlation at the Two-Particle Level
• Kinks in the dispersion of strongly correlated electrons
• 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
• From infinite to two dimensions through the functional renormalization group
• Nature of magnetic excitations in superconducting BaFe${}_{1.9}$Ni${}_{0.1}$As${}_2$
• Divergent Precursors of the Mott-Hubbard Transition at the Two-Particle Level
• Dynamical mean-field theory for pairing and spin gap in the attractive Hubbard model
• Local magnetic moments in iron and nickel at ambient and Earth's core conditions
• Quantum Quenches in the Hubbard Model: Time Dependent Mean Field Theory and The Role of Quantum Fluctuations
• Breakdown of traditional many-body theories for correlated electrons
• Dynamical vertex approximation in its parquet implementation: application to Hubbard nano-rings
• Energetic balance of the superconducting transition across the BCS-Bose E instein crossover in the attractive Hubbard model
• Pairing and Superconductivity from weak to strong coupling in the Attractive Hubbard model
• 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
• Divergences of the irreducible vertex functions in correlated metallic systems: Insights from the Anderson Impurity Model
• Quantum dynamical screening of the local magnetic moment in Fe-based superconductors
• Parquet decomposition calculations of the electronic self-energy
• Unphysical and Physical Solutions in Many-Body Theories: from Weak to Strong Correlation
• Solving the Parquet Equations for the Hubbard Model beyond Weak Coupling
• Practical consequences of Luttinger-Ward functional multivaluedness for cluster DMFT methods
• Generic optical excitations of correlated systems: $\pi$-tons
• Single-boson exchange decomposition of the vertex function
• Analytical investigation of singularities in two-particle irreducible vertex functions of the Hubbard atom
• Mott physics and collective modes: an atomic approximation of the four-particle irreducible functional
• Critical metal-insulator transition and divergence in a two-particle irreducible vertex in disordered and interacting electron systems
• Signature of antiferromagnetic long-range order in the optical spectrum of strongly correlated electron systems
• Self-energy and vertex functions from hybridization expansion continuous-time quantum Monte Carlo for impurity models with retarded interaction
• Low temperature properties of the infinite-dimensional attractive Hubbard model
• Continuous-time quantum Monte Carlo calculation of multi-orbital vertex asymptotics
• Efficient Bethe-Salpeter equations' treatment in dynamical mean-field theory
• Poor Man's Understanding of Kinks Originating from Strong Electronic Correlations
• Dynamical vertex approximation for the attractive Hubbard model
• Screened moments and absence of ferromagnetism in FeAl
• Charge-fluctuations in lightly hole-doped cuprates: effect of vertex corrections
• Kinks in the electronic specific heat
• Two-particle Fermi liquid parameters at the Mott transition: Vertex divergences, Landau parameters, and incoherent response in dynamical mean-field theory
• Momentum structure of the self-energy and its parametrization for the two-dimensional Hubbard model
• Finite-density corrections to the Unitary Fermi gas: A lattice perspective from Dynamical Mean-Field Theory
• Detecting a preformed pair phase: The response to a pairing forcing field

Cited by in corpus (33)

• Tracking the Footprints of Spin Fluctuations: A MultiMethod, MultiMessenger Study of the Two-Dimensional Hubbard Model
• 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
• Quantitative functional renormalization-group description of the two-dimensional Hubbard model
• Boson-Exchange Parquet Solver for dual fermions
• Multipoint correlation functions: spectral representation and numerical evaluation
• The Bethe-Salpeter equation at the critical end-point of the Mott transition
• Single boson exchange representation of the functional renormalization group for strongly interacting many-electron systems
• Characteristic Timescales of the Local Moment Dynamics in Hund's-metals
• How to read between the lines of electronic spectra: the diagnostics of fluctuations in strongly correlated electron systems
• Local Plaquette Physics as Key Ingredient of High-Temperature Superconductivity in Cuprates
• Highly nonperturbative nature of the Mott metal-insulator transition: Two-particle vertex divergences in the coexistence region
• Fulfillment of sum rules and Ward identities in the multiloop functional renormalization group solution of the Anderson impurity model
• 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
• Two-particle correlations and the metal-insulator transition: Iterated Perturbation Theory revisited
• 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
• Thermodynamic Stability at the Two-Particle Level
• General Shiba mapping for on-site four-point correlation functions
• Protection of Correlation-Induced Phase Instabilities by Exceptional Susceptibilities
• 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
• Second-order phase transitions and divergent linear response in dynamical mean-field theory
• Single-boson exchange formulation of the Schwinger-Dyson equation and its application to the functional renormalization group
• Non-Perturbative Feats in the Physics of Correlated Antiferromagnets
• Suppression of the charge fluctuations by nonlocal correlations close to the Mott transition
• Origin of misleading convergence in self-consistent many-electron theories: Fundamental aspects and practical implications
• Diagrammatic bosonization, aspects of criticality, and the Hohenberg-Mermin-Wagner theorem in parquet approaches
• Non-perturbative effects of short-range spatial correlations at the two-particle level