Electronic correlations and dynamical screening with ab initio quantum embedding

Abstract

First-principles descriptions of correlated quantum materials require a simultaneous treatment of strong local many-body effects and nonlocal dynamical screening. We present an efficient fully self-consistent implementation of $GW$+EDMFT that combines nonlocal effects at the $GW$ level with a non-perturbative treatment of local correlations within extended dynamical mean-field theory (EDMFT), while providing a controlled double-counting prescription. Crucially, self-consistency in both the Green's function and the dynamically screened interaction is essential to achieve a consistent description of screening processes across energy scales. The efficient computation of this self-consistent solution is enabled here by compressing two-particle correlation functions using interpolative separable density fitting (ISDF). Applying the scheme to the Mott insulator SrMnO$_3$ and the correlated metal LaNiO$_3$, we show that full self-consistency resolves the overscreening inherent to constrained-RPA approaches. By suppressing spurious low-energy screening channels, a Mott-insulating state in quantitative agreement with experiment is obtained for SrMnO$_3$. These results establish fully self-consistent $GW$+EDMFT as a predictive ab initio framework for strongly correlated quantum materials.

Figures (4)

• Figure 1: (a) Different types of screening processes, involving transitions between $\mathcal{B}$ and $\mathcal{C}$ (1), within $\mathcal{B}$ (2) and within $\mathcal{C}$ (3). The cRPA construction removes processes of type (3) from the polarisation, keeping (1) and (2). (b) In a Mott insulator, a gap opens within $\mathcal{C}$. Self-consistent $GW$+EDMFT improves the description of screening processes of type (1) which remedies the overscreening problem of cRPA. (c) Perturbative and non-perturbative contributions to the $\Psi$ functional in $GW$+EDMFT, within $\mathcal{B}$ and $\mathcal{C}$ respectively.
• Figure 2: (a) Local $GW$+EDMFT spectral functions for SrMnO$_3$. The EDMFT space is either the full Mn-3$d$ shell defined by $\mathcal{C}_5$ (thick lines) or the Mn-$t_{2g}$ states of $\mathcal{C}_3$ (dashed lines). For a fair comparison of both cases, the spectral functions are projected on the same set of very localised Wannier orbitals of $\mathcal{W}_{14}$. (b) Comparison to experimental PES and XAS data from Ref. smno_pes_Kim2010 (black dots). Thick lines correspond to calculations in which the full Mn $3d$ shell is included in the EDMFT impurity problem (same curve of the upper panel), while dashed lines denote a minimal Mn-$t_{2g}$ EDMFT sub-manifold extracted from $\mathcal{W}_{14}$.
• Figure 3: Local $GW$+EDMFT spectral functions for LaNiO$_3$ downfolded to MLWFs projected onto MLWFs constructed from a large energy window. Thick and dashed lines correspond respectively to the case where EDMFT encompasses the full Ni-$3d$ from $\mathcal{C}_5$ and minimal Ni-$e_g$ from $\mathcal{C}_2$.
• Figure 4: Local interactions for Mn-$t_{2g}$ and Ni-$e_g$ Wannier orbitals defined in the full $3d$ correlated manifold. Top panels report the local cRPA interaction and the effective local interactions $\mathcal{U}^{GW}$ and $\mathcal{U}^{\mathrm{EDMFT}}$ of the $\mathrm{sc}GW$ and $GW$+EDMFT converged solutions respectively. The inset shows the local EDMFT polarization compared to the corresponding RPA one. Bottom panels report the local bosonic propagators where electronic correlations are treated within perturbation theory and $GW$+EDMFT. Quantities plotted with yellow and red lines are linked through the same local Dyson equation.