Local correlation functions of arbitrary order for the Falicov-Kimball model

Abstract

Local n-particle vertex functions represent the crucial ingredient for all diagrammatic extensions of dynamical mean field theory (DMFT). Hitherto their application has been restricted -with a few exceptions- to the n=2-particle vertex while higher-order vertices have been neglected. In this paper we derive a general analytical expression for the n-particle (one-particle reducible) vertex of the Falicov-Kimball model (FKM). We observe that the magnitude of such vertex functions itself strongly increases with the particle-number n. On the other hand, their effect on generic Feynman diagrams remains rather moderate due to the damping effect of the Green's functions present in such diagrams. Nevertheless, they yield important contributions to the self-energy corrections calculated in diagrammatic extensions of DMFT as we explicitly demonstrate using the example of dual fermion (DF) calculations for the two-dimensional FKM at quarter filling of stationary f-electrons where corrections to the self-energy obtained from the three-particle vertex are indeed comparable in magnitude to corresponding corrections stemming from the two-particle vertex.

12 pages, 10 figures

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Cited by in corpus (12)

• Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory
• Multiloop functional renormalization group for general models
• Multiloop functional renormalization group that sums up all parquet diagrams
• Generic optical excitations of correlated systems: $\pi$-tons
• Analytical investigation of singularities in two-particle irreducible vertex functions of the Hubbard atom
• Role of three-particle vertex within dual fermion calculations
• Interpretable and unsupervised phase classification
• Dual fermion method as a prototype of generic reference-system approach for correlated fermions
• Momentum-Space Cluster Dual Fermion Method
• Gapless regime in the charge density wave phase of the finite dimensional Falicov-Kimball model
• Electronic transport through correlated electron systems with nonhomogeneous charge orderings
• The finite-difference parquet method: Enhanced electron-paramagnon scattering opens a pseudogap