We develop the extended dynamical mean-field theory (E-DMFT) with a view towards realistic applications. (1) We introduce an intuitive derivation of the E-DMFT formalism. By identifying the Hartree contributions before the E-DMFT treatment, it allows us to handle systems in symmetry-breaking phases within a simple formalism. (2) We make an implementation of E-DMFT through a real Hubbard--Stratonovich transformation to decouple the nonlocal two-particle interactions. We apply it to a three-dimensional $U\ensuremath{-}V$ model, with U the on-site and V the nearest-neighbor interactions, and investigate the behavior of the various Green's functions, especially the density susceptibility, as the density instability is approached. We obtain the phase diagram at a finite temperature. (3) We present a formalism incorporating E-DMFT with cellular DMFT. (4) We suggest an improvement of the E-DMFT approach by combining it with a generalized GW method. The method combines the local self-energy from E-DMFT and the nonlocal ones from the perturbative calculation of
GW. We apply the method to a one-dimensional $U\ensuremath{-}V$ model with two sublattices carrying different chemical potentials. By comparing with those from density matrix renormalization group calculations, we show that the results are shifted in the correct direction due to the
GW contributions. (5) In order to handle the generic Coulomb repulsion within E-DMFT, we describe a method to tailor E-DMFT so that the proper momentum dependence can be kept in general response functions.
Theoretical studies of semiconductors and band insulators are usually based on variants of the
GW method without full self-consistency, like single-shot
G0W0 or quasiparticle self-consistent
GW. Fully self-consistent
GW provides a poor description of the gap size and electronic structure due to the lack of vertex corrections. While it is hard to predict at which order corrections can be neglected, local vertex corrections to all orders can be consistently included by combining
GW with extended dynamical mean field theory (EDMFT). Here, we show that \textit{ab initio} multitier
GW+EDMFT calculations, which achieve full self-consistency in a suitably defined low-energy space, provide an accurate description of semiconductors and band insulators, comparable to the established methods which are typically used for this class of materials. Our results demonstrate that the range of applicability of
GW+EDMFT extends to weakly correlated systems, and they imply that despite the weak correlations, local vertex corrections are an important ingredient in the diagrammatic treatment of semiconductors and band insulators.
Extended dynamical mean-field theory (EDMFT) is insufficient to describe nonlocal effects in strongly correlated systems, since corrections to the mean-field solution are generally large. We present an efficient scheme for the construction of diagrammatic extensions of EDMFT that avoids the usual double-counting problem by using an exact change of variables (the Dual Boson formalism) to distinguish the correlations included in the dynamical mean-field solution and those beyond. With a computational efficiency comparable to the
EDMFT+GW approach, our scheme significantly improves on the charge order transition phase boundary in the extended Hubbard model.
Extended dynamical mean-field theory (EDMFT) is insufficient to describe non-local effects in strongly correlated systems, since corrections to the mean-field solution are generally large. We present an efficient scheme for the construction of diagrammatic extensions of EDMFT that avoids usual double counting problem by using an exact change of variables (the dual boson formalism) to distinguish the correlations included in the mean-field solution and those beyond. With a computational efficiency comparable to EDMFT+GW approach, our scheme significantly improves on the charge order transition phase boundary in the extended Hubbard model.
In electronic systems with long-range Coulomb interaction, the nonlocal Fock-exchange term has a band-widening effect. While this effect is included in combined many-body perturbation theory and dynamical mean field theory (DMFT) schemes, it is not taken into account in standard extended DMFT (EDMFT) calculations. Here, we include this instantaneous term in both approaches and investigate its effect on the phase diagram and dynamically screened interaction. We show that the largest deviations between previously presented EDMFT and
GW+EDMFT results originate from the nonlocal Fock term, and that the quantitative differences are especially large in the strong-coupling limit. Furthermore, we show that the charge-ordering phase diagram obtained in
GW+EDMFT methods for moderate interaction values is very similar to the one predicted by dual-boson methods that include the fermion-boson or four-point vertex.