Multitier self-consistent GW+EDMFT

Abstract

We discuss a parameter-free and computationally efficient ab initio simulation approach for moderately and strongly correlated materials, the multitier self-consistent GW +EDMFT method. This scheme treats different degrees of freedom, such as high-energy and low-energy bands, or local and nonlocal interactions, within appropriate levels of approximation, and provides a fully self-consistent description of correlation and screening effects in the solid. The ab initio input is provided by a one-shot G 0 W 0 calculation, while the strong-correlation effects originating from narrow bands near the Fermi level are captured by a combined GW plus extended dynamical mean-field (EDMFT) treatment. We present the formalism and technical details of our implementation and discuss some general properties of the effective EDMFT impurity action. In particular, we show that the retarded impurity interactions can have non-causal features, while the physical observables, such as the screened interactions of the lattice system, remain causal. As a first application, we present ab initio simulation results for SrMoO3, which demonstrate the existence of prominent plasmon satellites in the spectral function not obtainable within LDA+DMFT, and provide further support for our recent re-interpretation of the satellite features in the related cubic perovskite SrVO3. We then turn to stretched sodium as a model system to explore the performance of the multitier self-consistent GW +EDMFT method in situations with different degrees of correlation. While the results for the physical lattice spacing a0 show that the scheme is not very accurate for electron-gas like systems, because nonlocal corrections beyond GW are important, it does provide physically correct results in the intermediate correlation regime, and a Mott transition around a lattice spacing of 1.5a0. Remarkably, even though the Wannier functions in the stretched compound are less localized, and hence the bare interaction parameters are reduced, the self-consistently computed impurity interactions show the physically expected trend of an increasing interaction strength with increasing lattice spacing.

Recent Progress in First-Principles Methods for Computing the Electronic Structure of Correlated Materials

“…From Figure 8, it is therefore clear that the satellites should be interpreted as plasmons rather than Hubbard bands. This interpretation is supported by another material, SrMoO 3 , a 3d 2 system but with a similar electronic structure to SrVO 3 , which has a satellite feature below the quasiparticle peak that is not reproduced within the LDA+DMFT scheme within a physically reasonable range of U [97] but reproduced within the GW+EDMFT scheme [39].…”

“…This general consideration leads to the idea of multitier self-consistent GW+EDMFT [38,39]. Note that the tiers indicate the theoretical level and they are not the same as the subspaces.…”

“…Within the Multitier GW+EDMFT method [38,39], it is natural to use the narrow t 2g bands as both the correlated and intermediate subspace. Thus, within the t 2g subspace, the method reduces to a self-consistent GW+EDMFT method while the contributions from outside this subspace is included at the one-shot GW level.…”

“…This naturally leads to the GW+DMFT scheme [24], a combination of the GWA and DMFT. Several simplified approaches based on or related to the GW+DMFT scheme have since been proposed [25][26][27][28][29] and self-consistent calculations for model systems have been carried out [30][31][32][33][34][35][36][37], but, only recently, self-consistent GW+DMFT has been performed for real materials [38,39]. In the next section, a survey of the development leading to the present state-of-the-art schemes is described followed by a relatively detailed description of the GW+DMFT scheme, which is a basis for simplifications and further development.…”

“…In order to investigate the multitier approach further and understand in which regimes the GW+EDMFT method is applicable, the method was applied to stretched sodium in Ref. [39]. Sodium is an electron-gas like metal with weak correlations.…”