Non-perturbative effects of short-range spatial correlations at the two-particle level

Abstract

By means of cellular dynamical mean-field theory (CDMFT) we study how short-range correlations drive the breakdown of the self-consistent perturbation theory in two-dimensional systems and the most relevant physical consequences associated to it. To this aim, we first derive in a structured and consistent way the Bethe-Salpeter equation (BSE) formalism at the CDMFT level in all physical channels, explicitly addressing the important aspect of the related Ward identities. In this context, we perform systematic calculations of the BSE for the two-dimensional Hubbard model at half-filling at intermediate coupling. Our study illustrates how the divergence of a fundamental building block of the BSE in the charge channel, the two-particle irreducible vertex, systematically occurs at lower interactions than in the (purely local) DMFT case, due to short-range antiferromagnetic fluctuations. Further, the change of sign of the eigenvalues of the generalized charge susceptibility associated to the vertex divergences is identified as the essential prerequisite to drive, at larger interaction values, the physics of the Mott transition in two dimensions, as well as of the adjacent phase-separation instabilities.

28 pages, 12 figures

References in corpus (77)

• Quantum Cluster Theories
• Continuous Time Quantum Monte Carlo method for fermions
• Cellular Dynamical Mean Field Approach to Strongly Correlated Systems
• The Hubbard Model
• TRIQS: A Toolbox for Research on Interacting Quantum Systems
• Antiferromagnetism and d-wave superconductivity in cuprates: a uster DMFT study
• Non-perturbative many-body approach to the Hubbard model and single-particle pseudogap
• Self-energy-functional approach to systems of correlated electrons
• The Dynamical Cluster Approximation: Non-Local Dynamics of Correlated Electron Systems
• Cluster Dynamical Mean Field Theory of the Mott Transition
• Pseudogap induced by short-range spin correlations in a doped Mott insulator
• Continuous-time auxiliary field Monte Carlo for quantum impurity models
• Local Electronic Correlation at the Two-Particle Level
• Fate of the false Mott-Hubbard transition in two dimensions
• Tracking the Footprints of Spin Fluctuations: A MultiMethod, MultiMessenger Study of the Two-Dimensional Hubbard Model
• Cluster Dynamical Mean Field analysis of the Mott transition
• Landau Theory of the Finite Temperature Mott Transition
• Non-existence of the Luttinger-Ward functional and misleading convergence of skeleton diagrammatic series for Hubbard-like models
• Divergent Precursors of the Mott-Hubbard Transition at the Two-Particle Level
• Absence of a Slater Transition in The Two-Dimensional Hubbard Model
• Breakdown of traditional many-body theories for correlated electrons
• Extended crossover from Fermi liquid to quasi-antiferromagnet in the half-filled 2D Hubbard model
• 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
• Pseudogap and Mott Transition Studied by Cellular Dynamical Mean Field Theory
• One-particle irreducible functional approach - a new route to diagrammatic extensions of DMFT
• Impact of nonlocal correlations over different energy scales: A Dynamical Vertex Approximation study
• Stripes and spin-density waves in the doped two-dimensional Hubbard model: ground state phase diagram
• 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
• Signatures of the Mott transition in the antiferromagnetic state of the two-dimensional Hubbard model
• 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
• Cellular Dynamical Mean Field Theory for the 1D Extended Hubbard Model
• Collective Charge Excitations of Strongly Correlated Electrons, Vertex Corrections and Gauge Invariance
• Attractive effect of a strong electronic repulsion -- the physics of vertex divergences
• Practical consequences of Luttinger-Ward functional multivaluedness for cluster DMFT methods
• Single-boson exchange decomposition of the vertex function
• Analytical investigation of singularities in two-particle irreducible vertex functions of the Hubbard atom
• Spin and charge correlations across the metal-to-insulator crossover in the half-filled $2d$ Hubbard model
• Critical metal-insulator transition and divergence in a two-particle irreducible vertex in disordered and interacting electron systems
• The Fierz convergence criterion: a controlled approach to strongly-interacting systems with small embedded clusters
• The Bethe-Salpeter equation at the critical end-point of the Mott transition
• 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
• Tiling with triangles: parquet and $GW\gamma$ methods unified
• Conservation in two-particle self-consistent extensions of dynamical-mean-field-theory
• Efficient Bethe-Salpeter equations' treatment in dynamical mean-field theory
• Thermodynamic and information-theoretic description of the Mott transition in the two-dimensional Hubbard model
• Charge-fluctuations in lightly hole-doped cuprates: effect of vertex corrections
• Fermi liquid theory and divergences of the two-particle irreducible vertex in the periodic Anderson lattice
• Highly nonperturbative nature of the Mott metal-insulator transition: Two-particle vertex divergences in the coexistence region
• Real-space cluster dynamical mean-field theory: Center focused extrapolation on the one- and two particle level
• The Dynamical Mean Field Theory phase space extension and critical properties of the finite temperature Mott transition
• 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
• Fluctuations analysis of the spin susceptibility: Néel ordering revisited in dynamical mean field theory
• Specific heat maximum as a signature of Mott physics in the two-dimensional Hubbard model
• Mott transition and pseudogap of the square-lattice Hubbard model: results from center-focused cellular dynamical mean-field theory
• The effect of local magnetic moments on spectral properties and resistivity near the interaction- and doping induced Mott transitions
• Local Ward identities for collective excitations in fermionic systems with spontaneously broken symmetries
• Josephson lattice model for phase fluctuations of local pairs in copper-oxide superconductors
• 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
• Superconductivity in the two-dimensional Hubbard model with cellular dynamical mean-field theory: a quantum impurity model analysis
• 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
• Forestalled Phase Separation as the Precursor to Stripe Order
• Testing the parquet equations and the U(1) Ward identity for real-frequency correlation functions from the multipoint numerical renormalization group
• Non-Perturbative Feats in the Physics of Correlated Antiferromagnets
• 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