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

A First Principles Scheme for Calculating the Electronic Structure of Strongly Correlated Materials: GW+DMFT

We give a detailed description of a recently proposed first principles approach to the electronic structure of strongly correlated materials. The method combines the GW approximation with dynamical mean field theory. It is designed to describe Coulomb interactions and screening effects without adjustable parameters, thus avoiding the conceptual problems inherent to LDA+DMFT techniques.Comment: 18 pages, 3 figures, proceedings of the conference on "Coincidence Studies of Surfaces, Thin Films and Nanostructures", Ringberg castle, Sept. 2003. To be published by Wile

Correlation Effects in Orbital Magnetism

Orbital magnetization is known empirically to play an important role in several magnetic phenomena, such as permanent magnetism and ferromagnetic superconductivity. Within the recently developed ''modern theory of orbital magnetization'', theoretical insight has been gained into the nature of this often neglected contribution to magnetism, but is based on an underlying mean-field approximation. From this theory, a few treatments have emerged which also take into account correlations beyond the mean-field approximation. Here, we apply the scheme developed in a previous work [Phys. Rev. B ${\bf \text{93}}$, 161104(R) (2016)] to the Haldane-Hubbard model to investigate the effect of charge fluctuations on the orbital magnetization within the $GW$ approximation. Qualitatively, we are led to distinguish between two quite different situations: (i) When the lattice potential is larger than the nearest neighbor hopping, the correlations are found to boost the orbital magnetization. (ii) If the nearest neighbor hopping is instead larger than the lattice potential, the correlations reduce the magnetization.Comment: 8 pages, 9 figure

Correlation effects in solids from first principles

この論文は国立情報学研究所の電子図書館事業により電子化されました。サブゼミFirst principles calculations of bandstructures of crystals are usually based on one-particle theories where the electrons are assumed to move in some effective potential. The most commonly used method is based on density functional theory within the local density approximation (LDA). There is, however, no clear justification for interpreting the one-particle eigenvalues as the bandstructure. Indeed, the LDA failure to reproduce the experimental bandstructure is not uncommon. The most famous example is the bandgap problem in semiconductors and insulators where the LDA generally underestimates the gaps. A rigorous approach for calculating bandstructures or quasiparticle energies is provided by the Green function method. The main ingredient is the self-energy operator which acts like an effective potential but unlike in the LDA, it is nonlocal and energy dependent. The selfenergy contains the effects of exchange and correlations. An approximation to the self-energy which has proven fruitful in a wide range of materials is the so-called GW approximation (GWA). This approximation has successfully cured the LDA problems and has produced bandstructures with a rather high accuracy. For example, bandgaps in s-p semiconductors and insulators can be obtained typically to within 0.1-0.2 eV of the experimental values. Despite its success, the GWA has some problems. One of the most serious problems is its inadequacy to describe satellite structures in photoemission spectra. For example, multiple plasmon satellites observed in alkalis cannot be obtained by the GWA. Recently, a theory based on the cumulant expansion was proposed and shown to remedy this problem. Apart from plasmon satellites which are due to long-range correlations, there are also satellite structures arising from short-range correlations. This type of satellite cannot be described by the cumulant expansion. A t-matrix approach was proposed to account for this. Although traditionally the Green function method is used to calculate excitation spectra, groundstate energies can also be obtained from the Green function. Recent works on the electron gas have shown promising results and some approaches for calculating total energies will be discussed

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