Attractive effect of a strong electronic repulsion -- the physics of vertex divergences

Abstract

While the breakdown of the perturbation expansion for the many-electron problem has several formal consequences, here we unveil its physical effect: Flipping the sign of the effective electronic interaction in specific scattering channels. By decomposing local and uniform susceptibilities of the Hubbard model via their spectral representations, we prove how entering the non-perturbative regime causes an enhancement of the charge response, ultimately responsible for the phase-separation instabilities close to the Mott MIT. Our analysis opens a new route for understanding phase-transitions in the non-perturbative regime and clarifies why attractive effects emerging from a strong repulsion can induce phase-separations, but not s-wave pairing or charge-density wave instabilities.

arXiv comment6 pages, 4 Figures, Suppl. Mat.; accepted for publication in Physical Review Letters

References in corpus (41)

• Functional renormalization group approach to correlated fermion 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
• 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
• 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
• High-frequency asymptotics of the vertex function: diagrammatic parametrization and algorithmic implementation
• 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
• Mott physics and first-order transition between two metals in the normal state phase diagram of the two-dimensional Hubbard model
• Divergences of the irreducible vertex functions in correlated metallic systems: Insights from the Anderson Impurity Model
• Doping-driven Mott transition in the one-band Hubbard model
• Parquet approximation for the 4x4 Hubbard cluster
• Consistent partial bosonization of the extended Hubbard model
• 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
• Single-boson exchange decomposition of the vertex function
• Generic optical excitations of correlated systems: $\pi$-tons
• Mott physics and collective modes: an atomic approximation of the four-particle irreducible functional
• Analytical investigation of singularities in two-particle irreducible vertex functions of the Hubbard atom
• Critical metal-insulator transition and divergence in a two-particle irreducible vertex in disordered and interacting electron systems
• Derivation of exact flow equations from the self-consistent parquet relations
• Hund's induced Fermi-liquid instabilities and enhanced quasiparticle interactions
• Phase separation in the particle-hole asymmetric Hubbard model
• The Bethe-Salpeter equation at the critical end-point of the Mott transition
• Nonlocal correlations and spectral properties of the Falicov-Kimball model
• Interplay between local response and vertex divergences in many-fermion systems with on-site attraction
• Conservation in two-particle self-consistent extensions of dynamical-mean-field-theory
• Dynamical vertex approximation for the attractive Hubbard model
• Charge-fluctuations in lightly hole-doped cuprates: effect of vertex corrections
• Two-particle Fermi liquid parameters at the Mott transition: Vertex divergences, Landau parameters, and incoherent response in dynamical mean-field theory
• Thermodynamic consistency of the charge response in dynamical mean-field based approaches
• Critical Opalescence across the Doping Driven Mott Transition in Optical Lattices of Ultracold Atoms
• Specific heat maximum as a signature of Mott physics in the two-dimensional Hubbard model

Cited by in corpus (39)

• Tracking the Footprints of Spin Fluctuations: A MultiMethod, MultiMessenger Study of the Two-Dimensional Hubbard Model
• Fingerprints of the local moment formation and its Kondo screening in the generalized susceptibilities of many-electron problems
• Boson-Exchange Parquet Solver for dual fermions
• Multipoint correlation functions: spectral representation and numerical evaluation
• 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
• Highly nonperturbative nature of the Mott metal-insulator transition: Two-particle vertex divergences in the coexistence region
• Neutron Stars and Dark Matter
• Local Plaquette Physics as Key Ingredient of High-Temperature Superconductivity in Cuprates
• 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
• Mott Quantum Critical Points at finite doping
• 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
• Real-frequency quantum field theory applied to the single-impurity Anderson model
• Enhancement of charge instabilities in Hund's metals by the breaking of rotational symmetry
• Excitations and spectra from equilibrium real-time Green's functions
• 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
• CDMFT+HFD : an extension of dynamical mean field theory for nonlocal interactions applied to the single band extended Hubbard model
• Thermodynamic Stability at the Two-Particle Level
• Dual Bethe-Salpeter equation for the multi-orbital lattice susceptibility within dynamical mean-field theory
• Protection of Correlation-Induced Phase Instabilities by Exceptional Susceptibilities
• General Shiba mapping for on-site four-point correlation functions
• Compressing the two-particle Green's function using wavelets: Theory and application to the Hubbard atom
• Second-order phase transitions and divergent linear response in dynamical mean-field theory
• 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
• Origin of misleading convergence in self-consistent many-electron theories: Fundamental aspects and practical implications
• Long-term memory magnetic correlations in the Hubbard model: A dynamical mean-field theory analysis
• Non-perturbative effects of short-range spatial correlations at the two-particle level