We develop a diagrammatic approach with local and nonlocal self-energy diagrams, constructed from the local irreducible vertex. This approach includes the local correlations of dynamical mean field theory and long-range correlations beyond. It allows for example to describe (para-)magnons and weak localization effects-in strongly correlated systems. As a first application, we study the interplay between nonlocal antiferromagnetic correlations and the strong local correlations emerging in the vicinity of a Mott-Hubbard transition.
Strong electronic correlations pose one of the biggest challenges to solid state theory. Recently developed methods that address this problem by starting with the local, eminently important correlations of dynamical mean field theory (DMFT) are reviewed. In addition, nonlocal correlations on all length scales are generated through Feynman diagrams, with a local two-particle vertex instead of the bare Coulomb interaction as a building block. With these diagrammatic extensions of DMFT long-range charge-, magnetic-, and superconducting fluctuations as well as (quantum) criticality can be addressed in strongly correlated electron systems. An overview is provided of the successes and results achieved mainly for model Hamiltonians and an outline is given of future prospects for realistic material calculations. PACS numbers: 71.10.-w,71.10.Fd,71.27.+a CONTENTS 42 5. One and zero dimensions 43 B. Heavy fermions and Kondo lattice model (KLM) 44 C. Falicov-Kimball (FK) model 45 D. Models of Disorder 47 E. Non-local interactions and multiorbitals 48 V. Open source implementations 51 VI. Conclusion and outlook 51 References 53 arXiv:1705.00024v2 [cond-mat.str-el]
We use the dynamical vertex approximation (DΓA) with a Moriyaesque λ correction for studying the impact of antiferromagnetic fluctuations on the spectral function of the Hubbard model in two and three dimensions. Our results show the suppression of the quasiparticle weight in three dimensions and dramatically stronger impact of spin fluctuations in two dimensions where the pseudogap is formed at low enough temperatures. Even in the presence of the Hubbard subbands, the origin of the pseudogap at weak-to-intermediate coupling is in the splitting of the quasiparticle peak. At stronger coupling (closer to the insulating phase) the splitting of Hubbard subbands is expected instead. The k-dependence of the self energy appears to be also much more pronounced in two dimensions as can be observed in the k-resolved DΓA spectra, experimentally accessible by angular resolved photoemission spectroscopy in layered correlated systems.
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