Highly nonperturbative nature of the Mott metal-insulator transition: Two-particle vertex divergences in the coexistence region

Abstract

We thoroughly analyze the divergences of the irreducible vertex functions occurring in the charge channel of the half-filled Hubbard model in close proximity to the Mott metal-insulator transition (MIT). In particular, by systematically performing dynamical mean-field theory (DMFT) calculations on the two-particle level, we determine the location and the number of the vertex divergences across the whole coexistence region adjacent to the first-order metal-to-insulator transition. We find that the lines in the parameter space, along which the vertex divergences occur, display a qualitatively different shape in the coexisting metallic and insulating phase, which is also associated to an abrupt jump of the number of divergences across the MIT. Physically, the systematically larger number of divergences on the insulating side of the transition reflects the sudden suppression of local charge fluctuation at the MIT. Further, a systematic analysis of the results demonstrates that the number of divergence lines increases as a function of the inverse temperature $\beta =(k_{\mathrm{B}}T{)}^{-1}$ by approaching the Mott transition in the zero temperature limit. This makes it possible to identify the zero-temperature MIT as an accumulation point of an infinite number of vertex divergence lines, unveiling the highly nonperturbative nature of the underlying transition.

arXiv comment16 pages, 12 figures

References in corpus (57)

• Continuous-time Monte Carlo methods for quantum impurity models
• Quantum Cluster Theories
• A continuous-time solver for quantum impurity models
• 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
• Fate of the false Mott-Hubbard transition in two dimensions
• 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
• From infinite to two dimensions through the functional renormalization group
• Divergent Precursors of the Mott-Hubbard Transition at the Two-Particle Level
• Efficient perturbation theory for quantum lattice models
• High-frequency asymptotics of the vertex function: diagrammatic parametrization and algorithmic implementation
• Dynamical vertex approximation in its parquet implementation: application to Hubbard nano-rings
• Breakdown of traditional many-body theories for correlated electrons
• 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
• The magnetic excitation spectra in BaFe${}_2$As${}_2$: a two-particle approach within DFT+DMFT
• 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
• Unphysical and Physical Solutions in Many-Body Theories: from Weak to Strong Correlation
• Parquet decomposition calculations of the electronic self-energy
• Antiferromagnetic and d-wave pairing correlations in the strongly interacting two-dimensional Hubbard model from the functional renormalization group
• Fingerprints of the local moment formation and its Kondo screening in the generalized susceptibilities of many-electron problems
• Shifted-Action Expansion and Applicability of Dressed Diagrammatic Schemes
• 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
• 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
• Electron spectra close to a metal-to-insulator transition
• Critical metal-insulator transition and divergence in a two-particle irreducible vertex in disordered and interacting electron systems
• Boson-Exchange Parquet Solver for dual fermions
• Continuous-time Quantum Monte Carlo using Worm Sampling
• Correlated starting points for the functional renormalization group
• 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
• Skeleton series and multivaluedness of the self-energy functional in zero space-time dimensions
• Self-consistent ladder D$\Gamma$A approach
• Spin dynamics of itinerant electrons: local magnetic moment formation and Berry phase
• 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
• Charge-fluctuations in lightly hole-doped cuprates: effect of vertex corrections
• Density of states near the Mott-Hubbard transition in the limit of large dimensions
• Fermi liquid theory and divergences of the two-particle irreducible vertex in the periodic Anderson lattice
• Fulfillment of sum rules and Ward identities in the multiloop functional renormalization group solution of the Anderson impurity model
• State- and superstate-sampling in hybridization-expansion continuous-time quantum Monte Carlo
• 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
• Generic susceptibilities of the half-filled Hubbard model in infinite dimensions
• 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
• The effect of local magnetic moments on spectral properties and resistivity near the interaction- and doping induced Mott transitions

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• Non-perturbative intertwining between spin and charge correlations: A "smoking gun" single-boson-exchange result
• Two-particle calculations with quantics tensor trains: Solving the parquet equations
• Mott transition and pseudogap of the square-lattice Hubbard model: results from center-focused cellular dynamical mean-field theory
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• Spectral representation of Matsubara n-point functions: Exact kernel functions and applications
• Thermodynamic Stability at the Two-Particle Level
• 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
• Analytic continuation of multipoint correlation functions
• Effective enhancement of the electron-phonon coupling driven by nonperturbative electronic density fluctuations
• 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
• Disentangling real space fluctuations: the diagnostics of metal-insulator transitions beyond single-particle spectral functions
• Origin of misleading convergence in self-consistent many-electron theories: Fundamental aspects and practical implications
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