Nonlocal correlations and spectral properties of the Falicov-Kimball model

Abstract

We derive an analytical expression for the local two-particle vertex of the Falicov-Kimball model, including its dependence on all three frequencies, the full vertex and all reducible vertices. This allows us to calculate the self energy in diagrammatic extensions of dynamical mean field theory, specifically in the dual fermion and the one-particle irreducible approach. Non-local correlations are thence included and originate here from charge density wave fluctuations. At low temperatures and in two dimensions, they lead to a larger self energy contribution at low frequencies and a more insulating spectrum.

12 pages, 10 figures

References in corpus (11)

• Dynamical vertex approximation - a step beyond dynamical mean field theory
• Variational cluster approach to correlated electron systems in low dimensions
• Mott physics and spin fluctuations: a unified framework
• Dual fermion approach to the two-dimensional Hubbard model: Antiferromagnetic fluctuations and Fermi arcs
• Influence of Spatial Correlations in Strongly Correlated Electron Systems: Extension to Dynamical Mean Field Approximation
• Non-perturbative landscape of the Mott-Hubbard transition: Multiple divergence lines around the critical endpoint
• Mechanisms of finite temperature magnetism in the three-dimensional Hubbard model
• FLEX+DMFT approach to the $d$-wave superconducting phase diagram of the two-dimensional Hubbard model
• Hidden physics in the dual-fermion approach - a special case of a non-local expansion scheme
• The effect of six-point one-particle reducible local interactions in the dual fermion approach
• Vertex corrections to the mean-field electrical conductivity in strongly disordered electron systems

Cited by in corpus (41)

• Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory
• 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
• Divergences of the irreducible vertex functions in correlated metallic systems: Insights from the Anderson Impurity Model
• Parquet decomposition calculations of the electronic self-energy
• 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
• Analytical investigation of singularities in two-particle irreducible vertex functions of the Hubbard atom
• Boson-Exchange Parquet Solver for dual fermions
• Interaction-tuned Anderson versus Mott localization
• Worm Improved Estimators in Continuous-time Quantum Monte Carlo
• Diagrammatic Monte Carlo 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
• Fermion-boson vertex within Dynamical Mean-Field Theory
• How to read between the lines of electronic spectra: the diagnostics of fluctuations in strongly correlated electron systems
• Fulfillment of sum rules and Ward identities in the multiloop functional renormalization group solution of the Anderson impurity model
• Highly nonperturbative nature of the Mott metal-insulator transition: Two-particle vertex divergences in the coexistence region
• Interpretable and unsupervised phase classification
• The dynamical vertex approximation for many-electron systems with spontaneously broken SU(2)-symmetry
• Towards ab initio calculations with the dynamical vertex approximation
• Non-perturbative intertwining between spin and charge correlations: A "smoking gun" single-boson-exchange result
• Parquet dual fermion approach for the Falicov-Kimball model
• Real-frequency quantum field theory applied to the single-impurity Anderson model
• Momentum-Space Cluster Dual Fermion Method
• Non-perturbative series expansion of Green's functions: The Anatomy of Resonant Inelastic X-Ray Scattering in Doped Hubbard Model
• Single-boson exchange functional renormalization group application to the two-dimensional Hubbard model at weak coupling
• Complementary views on electron spectra: From Fluctuation Diagnostics to real space correlations
• Local correlation functions of arbitrary order for the Falicov-Kimball model
• Extended Falicov-Kimball model: Exact solution for finite temperatures
• Extended Falicov-Kimball model: exact solution for the ground state
• The one-dimensional Long-Range Falikov-Kimball Model: Thermal Phase Transition and Disorder-Free Localisation
• Symmetric improved estimators for multipoint vertex functions
• Gapless regime in the charge density wave phase of the finite dimensional Falicov-Kimball model
• Protection of Correlation-Induced Phase Instabilities by Exceptional Susceptibilities
• Second-order dual fermion for multi-orbital systems
• Electronic transport through correlated electron systems with nonhomogeneous charge orderings
• Single-boson exchange formulation of the Schwinger-Dyson equation and its application to the functional renormalization group