Local Electronic Correlation at the Two-Particle Level

Details Local Electronic Correlation at the Two-Particle Level Local Electronic Correlation at the Two-Particle Level

2012-02-13

arxiv.org/abs/1202.2796v2

Physics

Condensed Matter

Strongly Correlated Electrons

24 pages, 24 Figures

Scientific paper

Electronic correlated systems are often well described by dynamical mean field theory (DMFT). While DMFT is an exact self-consistent theory in the limit of infinite coordination number or dimensions, when applying it as an approximation to finite-dimensional systems, its self-consistency is guaranteed at the one-particle level only, i.e., for the local Green function and self-energy. However, extremely valuable information is also enclosed in the local two-particle Green functions and vertices. In fact, even at the DMFT level, mastering the calculation of two-particle quantities is crucial to compute momentum-dependent response functions that can be compared directly with experiments. Moreover, the knowledge of the local two-particle Green function represents the main ingredient for including non-local spatial correlations at all length scales by means of diagrammatic extensions of DMFT, such as the dynamical vertex approximation (D$\Gamma$A) or the dual fermion approach. As hitherto the investigation of local two-particle properties has been merely sporadic, we present here a systematic analysis of the local reducible and irreducible two-particle vertex functions for the Hubbard model at the DMFT level in the context of an unified diagrammatic formalism, providing an interpretation of the observed frequency structures in terms of perturbation theory results and of the mapping onto the attractive Hubbard model.

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