Extensions of DMFT to the Nonlocal Case

Corey Melnick, P. Sémon, Kwangmin Yu +3 more

Volodymyr Turkowski

Ryota Mizuno, Masayuki Ochi, Kazuhiko Kuroki

The two-particle vertex function is crucial for the diagrammatic extensions beyond DMFT for the nonlocal fluctuation. However, estimating the two-particle quantities is still a challenging task. In this study, we propose a simplification of the local two-particle full vertex and, using the simplified full vertex, we develop two methods to take into account the nonlocal fluctuation. We apply these methods to several models and confirm that our methods can capture important behaviors such as the pseudo gap in the DMFT + nonlocal calculation. In addition, the numerical costs are largely reduced compared to the conventional methods.

F. Aryasetiawan, Fredrik Nilsson

In this last chapter, very recent promising developments beyond GW+EDMFT by taking into account nonlocal vertex corrections beyond the RPA are described. The first development is the dual fermion and boson approach in which DMFT is used as a starting point for a perturbation expansion of the nonlocal self-energy. This approach is very general and in its lowest similar to the GW+EDMFT scheme. The second development is the TRILEX approach based on the extension of the GW+EDMFT scheme to include higher-order correlation or vertex functions in the self-consistency condition. Like the GW+EDMFT scheme, this approach maintains the basic concept of DMFT in that local projected quantities are made self-consistent. In this way, nonlocal spin fluctuations missing in the GW+EDMFT scheme are incorporated. The third development is the dynamical vertex approximation method, which can be considered as a generalization of DMFT assuming the locality of the two-particle irreducible vertex. This chapter closes with a summary.

C. W. Rietdijk

Volodymyr Turkowski