General Shiba mapping for on-site four-point correlation functions

Abstract

By applying the Shiba mapping on the two particle level, we derive the relation between the local four-point correlation functions of bipartite lattice models with on-site electronic repulsion and those of the corresponding models with attractive interaction in the most general setting. In particular, we extend the results of [Phys. Rev. B, 101, 155148 (2020)], which were limited to the rather specific situation of the static limit in strictly particle-hole symmetric models, (i) by explicitly including both magnetic field and different values of the chemical potentials, and (ii) by considering the full dependence of the generalized susceptibilities on the transfer (bosonic) Matsubara frequency. The derived formalism is then applied, as a relevant benchmark, to the Hubbard atom, by investigating the general properties of the divergences of its irreducible vertex functions as a function of chemical potential and applied magnetic field. The resulting phase-diagrams provide an insightful compass for future studies of the breakdown of the self-consistent perturbation expansion beyond high-symmetric regimes.

arXiv commentSubmitted version, 16 Pages, 6 Figures, + Appendix

References in corpus (47)

• Quantum Cluster Theories
• Cellular Dynamical Mean Field Approach to 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
• 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
• Nature of magnetic excitations in superconducting BaFe${}_{1.9}$Ni${}_{0.1}$As${}_2$
• 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
• Local magnetic moments in iron and nickel at ambient and Earth's core conditions
• Strong-Coupling Perturbation Theory of the Hubbard Model
• High-frequency asymptotics of the vertex function: diagrammatic parametrization and algorithmic implementation
• Breakdown of traditional many-body theories for correlated electrons
• 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
• Parquet decomposition calculations of the electronic self-energy
• Unphysical and Physical Solutions in Many-Body Theories: from Weak to Strong Correlation
• Shifted-Action Expansion and Applicability of Dressed Diagrammatic Schemes
• 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
• 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
• Boson-Exchange Parquet Solver for dual fermions
• Multipoint correlation functions: spectral representation and numerical evaluation
• Self-energy and vertex functions from hybridization expansion continuous-time quantum Monte Carlo for impurity models with retarded interaction
• Charge transport in the Hubbard model at high temperatures: triangular versus square lattice
• Phase separation in the particle-hole asymmetric Hubbard model
• The Bethe-Salpeter equation at the critical end-point of the Mott transition
• Mechanism of Superconductivity in the Hubbard Model at Intermediate Interaction Strength
• Interplay between local response and vertex divergences in many-fermion systems with on-site attraction
• Efficient Bethe-Salpeter equations' treatment in dynamical mean-field theory
• Dynamical vertex approximation for the attractive Hubbard model
• Charge-fluctuations in lightly hole-doped cuprates: effect of vertex corrections
• 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
• Highly nonperturbative nature of the Mott metal-insulator transition: Two-particle vertex divergences in the coexistence region
• 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
• Dynamically enhanced magnetic incommensurability: Effects of local dynamics on non-local spin-correlations in a strongly correlated metal
• Charge fluctuations, hydrodynamics and transport in the square-lattice Hubbard model
• Protection of Correlation-Induced Phase Instabilities by Exceptional Susceptibilities
• Analytic continuation of multipoint correlation functions
• Second-order phase transitions and divergent linear response in dynamical mean-field theory
• Physical and unphysical regimes of self-consistent many-body perturbation theory

Cited by in corpus (7)

• Two-particle calculations with quantics tensor trains: Solving the parquet equations
• Thermodynamic Stability at the Two-Particle Level
• Effective enhancement of the electron-phonon coupling driven by nonperturbative electronic density fluctuations
• Intertwined fluctuations and isotope effects in the Hubbard-Holstein model on the square lattice from functional renormalization
• Non-Perturbative Feats in the Physics of Correlated Antiferromagnets
• Origin of misleading convergence in self-consistent many-electron theories: Fundamental aspects and practical implications
• Non-perturbative effects of short-range spatial correlations at the two-particle level