One-particle irreducible functional approach - a new route to diagrammatic extensions of DMFT

Abstract

We present an approach which is based on the one-particle irreducible (1PI) generating functional formalism and includes electronic correlations on all length-scales beyond the local correlations of dynamical mean field theory (DMFT). This formalism allows us to unify aspects of the dynamical vertex approximation (D\GammaA) and the dual fermion (DF) scheme, yielding a consistent formulation of non-local correlations at the one- and two-particle level beyond DMFT within the functional integral formalism. In particular, the considered approach includes one-particle reducible contributions from the three- and more-particle vertices in the dual fermion approach, as well as some diagrams not included in the ladder version of D\GammaA. To demonstrate the applicability and physical content of the 1PI approach, we compare the diagrammatics of 1PI, DF and D\GammaA, as well as the numerical results of these approaches for the half-filled Hubbard model in two dimensions.

36 pages, 12 figures, updated version

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Cited by in corpus (79)

• Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory
• Fate of the false Mott-Hubbard transition in two dimensions
• w2dynamics: Local one- and two-particle quantities from dynamical mean field theory
• Fluctuation diagnostics of the electron self-energy: Origin of the pseudogap physics
• From infinite to two dimensions through the functional renormalization group
• Beyond extended dynamical mean-field theory: Dual boson approach to the two-dimensional extended Hubbard model
• 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
• Ab initio dynamical vertex approximation
• Mott physics and spin fluctuations: a functional viewpoint
• Multiloop functional renormalization group that sums up all parquet diagrams
• Multiloop functional renormalization group for general models
• Impact of nonlocal correlations over different energy scales: A Dynamical Vertex Approximation study
• Divergences of the irreducible vertex functions in correlated metallic systems: Insights from the Anderson Impurity Model
• On the dangers of partial diagrammatic summations: Benchmarks for the two-dimensional Hubbard model in the weak-coupling regime
• Plasmons in strongly correlated systems: spectral weight transfer and renormalized dispersion
• Parquet decomposition calculations of the electronic self-energy
• Collective Charge Excitations of Strongly Correlated Electrons, Vertex Corrections and Gauge Invariance
• Mechanisms of finite temperature magnetism in the three-dimensional Hubbard model
• Merging GW with DMFT and non-local correlations beyond
• Generic optical excitations of correlated systems: $\pi$-tons
• Why the critical temperature of high-$T_{\mathrm{c}}$ cuprate superconductors is so low: The importance of the dynamical vertex structure
• Intermediate Coupling Model of the Cuprates
• Self-consistent Dual Boson approach to single-particle and collective excitations in correlated systems
• Quantum criticality with a twist - interplay of correlations and Kohn anomalies in three dimensions
• Critical metal-insulator transition and divergence in a two-particle irreducible vertex in disordered and interacting electron systems
• FLEX+DMFT approach to the $d$-wave superconducting phase diagram of the two-dimensional Hubbard model
• Diagrammatic Monte Carlo approach for diagrammatic extensions of dynamical mean-field theory -- convergence analysis of the dual fermion technique
• Worm Improved Estimators in Continuous-time Quantum Monte Carlo
• Importance of d-p Coulomb interaction for high T${}_C$ cuprates and other oxides
• Diagrammatic Monte Carlo for Dual Fermions
• Self-energy and vertex functions from hybridization expansion continuous-time quantum Monte Carlo for impurity models with retarded interaction
• Continuous-time Quantum Monte Carlo using Worm Sampling
• Dual parquet scheme for the two-dimensional Hubbard model: modelling low-energy physics of high-$T_c$ cuprates with high momentum resolution
• Correlated starting points for the functional renormalization group
• Nonlocal correlations and spectral properties of the Falicov-Kimball model
• From local to non-local correlations: the Dual Boson perspective
• Overcomplete compact representation of two-particle Green's functions
• Conservation in two-particle self-consistent extensions of dynamical-mean-field-theory
• Effective crystal field and Fermi surface topology: a comparison of d- and dp-orbital models
• Efficient Bethe-Salpeter equations' treatment in dynamical mean-field theory
• Continuous-time quantum Monte Carlo calculation of multi-orbital vertex asymptotics
• Dynamical vertex approximation for the two-dimensional Hubbard model
• Dynamical vertex approximation for the attractive Hubbard model
• On the separability of dynamical and non-local correlations in three dimensions
• Quantum criticality in the two-dimensional periodic Anderson model
• Role of three-particle vertex within dual fermion calculations
• Sparse sampling and tensor network representation of two-particle Green's functions
• Hidden physics in the dual-fermion approach - a special case of a non-local expansion scheme
• Real-space cluster dynamical mean-field theory: Center focused extrapolation on the one- and two particle level
• Realistic theory of electronic correlations in nanoscopic systems
• The dynamical vertex approximation for many-electron systems with spontaneously broken SU(2)-symmetry
• Metal-insulator transition in the 2D Hubbard model: dual fermion approach with the Lanczos exact diagonalization
• Parquet approximation for molecules: spectrum and optical conductivity of the Pariser-Parr-Pople model
• Towards ab initio calculations with the dynamical vertex approximation
• Thermodynamic consistency of the charge response in dynamical mean-field based approaches
• Momentum structure of the self-energy and its parametrization for the two-dimensional Hubbard model
• The AbinitioD$\Gamma$A Project v1.0: Non-local correlations beyond and susceptibilities within dynamical mean-field theory
• Strongly correlated superconductivity with long-range spatial fluctuations
• Extended regime of coexisting metallic and insulating phases in a two-orbital electronic system
• Fluctuations analysis of the spin susceptibility: Néel ordering revisited in dynamical mean field theory
• Two-particle-correlations in a functional renormalization group scheme using a dynamical mean-field theory approach
• Non-perturbative series expansion of Green's functions: The Anatomy of Resonant Inelastic X-Ray Scattering in Doped Hubbard Model
• Complementary views on electron spectra: From Fluctuation Diagnostics to real space correlations
• Strongly correlated electrons: Analytic mean-field theories with two-particle self-consistency
• Local correlation functions of arbitrary order for the Falicov-Kimball model
• Impact of self-consistency in dual fermion calculations
• Non-linear responses and three-particle correlators in correlated electron systems exemplified by the Anderson impurity model
• Electronic correlations and long-range magnetic ordering in NiO tuned by pressure
• Consistency of potential energy in the dynamical vertex approximation
• Suppression of the charge fluctuations by nonlocal correlations close to the Mott transition
• Functional renormalization-group approaches, one-particle (ir)reducible with respect to local Green functions, using the dynamical mean-field theory as a starting point
• Computing local multipoint correlators using the numerical renormalization group
• Quantitative Description of Strongly Correlated Materials by Combining Downfolding Techniques and Tensor Networks
• Non-perturbative effects of short-range spatial correlations at the two-particle level
• Dynamical Cluster Approximation Study of Electron Localization in the Extended Hubbard Model