Screened Coulomb interaction in the maximally localized Wannier basis

We discuss a maximally localized Wannier function approach for constructing lattice models from first-principles electronic structure calculations, where the effective Coulomb interactions are calculated in the constrained random-phase-approximation. The method is applied to the 3d transition metals and a perovskite (SrVO_3). We also optimize the Wannier functions by unitary transformation so that U is maximized. Such Wannier functions unexpectedly turned out to be very close to the maximally localized ones.Comment: 22 pages, 6 figure

Method for calculating the electronic structure of correlated materials from a truly first-principles LDA+U scheme

We present a method for calculating the electronic structure of correlated materials based on a truly first-principles LDA+U scheme. Recently we suggested how to calculate U from first-principles, using a method which we named constrained RPA (cRPA). The input is simply the Kohn-Sham eigenfunctions and eigenvalues obtained within the LDA. In our proposed self-consistent LDA+U scheme, we calculate the LDA+U eigenfunctions and eigenvalues and use these to extract U. The updated U is then used in the next iteration to obtain a new set of eigenfunctions and eigenvalues and the iteration is continued until convergence is achieved. The most significant result is that our numerical approach is indeed stable: it is possible to find the effective exchange and correlation interaction matrix in a self-consistent way, resulting in a significant improvement over the LDA results, regarding both the bandgap in NiO and the f-band exchange spin-splitting in Gd, but some discrepancies still remain.Comment: 11 pages, 4 figure

Spin-dependent Hedin's equations

Hedin's equations for the electron self-energy and the vertex were originally derived for a many-electron system with Coulomb interaction. In recent years it has been increasingly recognized that spin interactions can play a major role in determining physical properties of systems such as nanoscale magnets or of interfaces and surfaces. We derive a generalized set of Hedin's equations for quantum many-body systems containing spin interactions, e.g. spin-orbit and spin-spin interactions. The corresponding spin-dependent GW approximation is constructed.Comment: 5 pages, 1 figur

The effects of k-dependent self-energy in the electronic structure of correlated materials

It is known from self-energy calculations in the electron gas and sp materials based on the GW approximation that a typical quasiparticle renormalization factor (Z factor) is approximately 0.7-0.8. Band narrowing in electron gas at rs = 4 due to correlation effects, however, is only approximately 10%, significantly smaller than the Z factor would suggest. The band narrowing is determined by the frequency-dependent self-energy, giving the Z factor, and the momentum-dependent or nonlocal self-energy. The results for the electron gas point to a strong cancellation between the effects of frequency- and momentum-dependent self-energy. It is often assumed that for systems with a nar- row band the self-energy is local. In this work we show that even for narrow-band materials, such as SrVO3, the nonlocal self-energy is important.Comment: 7 pages, 6 figure

Multitier self-consistent GWGW+EDMFT

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 $G^0W^0$ 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. 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 $a_0$ 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 $1.5a_0$. 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.Comment: 22 pages, 19 figure

Competition between Energy-Dependent U and Nonlocal Self-Energy in Correlated Materials: Application of GW+DMFT to SrVO3

We describe an implementation of the GW+DMFT method and apply it to calculate the electronic structure of SrVO₃. Our results show that there is a strong competition between the frequency-dependent Hubbard U and the non-local self-energy via the GW approximation. It is crucial to take into account these two aspects in order to obtain an accurate and coherent picture of the quasi-particle band structure and satellite features of SrVO₃. Our main conclusion is that the GW+DMFT results for SrVO₃ are not attainable within the GW approximation or the LDA+DMFT scheme

The alpha-gamma transition of Cerium is entropy-driven

We emphasize, on the basis of experimental data and theoretical calculations, that the entropic stabilization of the gamma-phase is the main driving force of the alpha-gamma transition of cerium in a wide temperature range below the critical point. Using a formulation of the total energy as a functional of the local density and of the f-orbital local Green's functions, we perform dynamical mean-field theory calculations within a new implementation based on the multiple LMTO method, which allows to include semi-core states. Our results are consistent with the experimental energy differences and with the qualitative picture of an entropy-driven transition, while also confirming the appearance of a stabilization energy of the alpha phase as the quasiparticle Kondo resonance develops.Comment: 5 pages, 6 figure