Dipole matrix element approach vs. Peierls approximation for optical conductivity

We develop a computational approach for calculating the optical conductivity in the augmented plane wave basis set of Wien2K and apply it for thoroughly comparing the full dipole matrix element calculation and the Peierls approximation. The results for SrVO3 and V2O3 show that the Peierls approximation, which is commonly used in model calculations, works well for optical transitions between the d orbitals. In a typical transition metal oxide, these transitions are solely responsible for the optical conductivity at low frequencies. The Peierls approximation does not work, on the other hand, for optical transitions between p- and d-orbitals which usually became important at frequencies of a few eVsComment: 11 pages, 4 figure

Divergences of the irreducible vertex functions in correlated metallic systems: Insights from the Anderson Impurity Model

In this work, we analyze in detail the occurrence of divergences in the irreducible vertex functions for one of the fundamental models of many-body physics: the Anderson impurity model (AIM). These divergences -- a surprising hallmark of the breakdown of many-electron perturbation theory -- have been recently observed in several contexts, including the dynamical mean-field solution of the Hubbard model. The numerical calculations for the AIM presented in this work, as well as their comparison with the corresponding results for the Hubbard model, allow us to clarify several open questions about the origin and the properties of vertex divergences in a particularly interesting context, the correlated metallic regime at low-temperatures. Specifically, our analysis (i) rules out explicitly the transition to a Mott insulating phase, but not the more general suppression of charge fluctuations (proposed in [Phys.\,Rev.\,B {\bf 93},\,245102\,(2016)]), as a necessary condition for the occurrence of vertex divergences, (ii) clarifies their relation with the underlying Kondo physics, and, eventually, (iii) individuates which divergences might also appear on the real frequency axis in the limit of zero temperature, through the discovered scaling properties of the singular eigenvectors.Comment: 16 pages, 13 figures, published versio

Electronic structure of CeRu4Sn6: a density functional plus dynamical mean field theory study

The Kondo system CeRu$_4$Sn$_6$ shows a strong anisotropy in its electric, optic and magnetic properties. We employ density functional theory plus dynamical mean field theory and show that the predominant Ce-$f$ state has total angular moment $J=5/2$ and $z$-component $m_J=\pm 1/2$ in agreement with recent X-ray absorption experiments. Even though CeRu$_4$Sn$_6$ has the direct gap of a Kondo insulator through most of the Brillouin zone it remains weakly metallic. This is because of (i) a band crossing in the $z$-direction and (ii) a negative indirect gap.Comment: 6 pages, 9 figure

Woptic: optical conductivity with Wannier functions and adaptive k-mesh refinement

We present an algorithm for the adaptive tetrahedral integration over the Brillouin zone of crystalline materials, and apply it to compute the optical conductivity, dc conductivity, and thermopower. For these quantities, whose contributions are often localized in small portions of the Brillouin zone, adaptive integration is especially relevant. Our implementation, the woptic package, is tied into the wien2wannier framework and allows including a many-body self energy, e.g. from dynamical mean-field theory (DMFT). Wannier functions and dipole matrix elements are computed with the DFT package Wien2k and Wannier90. For illustration, we show DFT results for fcc-Al and DMFT results for the correlated metal SrVO$_3$.Comment: 14 pages, 10 figures. Changes from v1: corrected prefactor of optical conductivity; minor changes for readabilit

Merging GW with DMFT and non-local correlations beyond

We review recent developments in electronic structure calculations that go beyond state-of-the-art methods such as density functional theory (DFT) and dynamical mean field theory (DMFT). Specifically, we discuss the following methods: GW as implemented in the Vienna {\it ab initio} simulation package (VASP) with the self energy on the imaginary frequency axis, GW+DMFT, and ab initio dynamical vertex approximation (D$\Gamma$A). The latter includes the physics of GW, DMFT and non-local correlations beyond, and allows for calculating (quantum) critical exponents. We present results obtained by the three methods with a focus on the benchmark material SrVO$_3$.Comment: tutorial review submitted to EPJ-ST (scientific report of research unit FOR 1346); 11 figures 27 page

Dichotomy between large local and small ordered magnetic moment in Iron-based superconductors

We study a four band model for iron-based superconductors within local density approximation + dynamical mean field theory (LDA+DMFT). This successfully reproduces the results of models which take As p degrees of freedom explicitly into account and has several physical advantages over the standard five d-band model. Our findings reveal that the new superconductors are more strongly correlated than their single-particle properties suggest. Two-particle correlation functions unveil the dichotomy between local and ordered magnetic moments in these systems, calling for further experiments to better resolve the short time scale spin dynamics.Comment: 4 pages, 3 figure

Energy Spectrum of Quasi-Geostrophic Turbulence

We consider the energy spectrum of a quasi-geostrophic model of forced, rotating turbulent flow. We provide a rigorous a priori bound E(k) <= Ck^{-2} valid for wave numbers that are smaller than a wave number associated to the forcing injection scale. This upper bound separates this spectrum from the Kolmogorov-Kraichnan k^{-{5/3}} energy spectrum that is expected in a two-dimensional Navier-Stokes inverse cascade. Our bound provides theoretical support for the k^{-2} spectrum observed in recent experiments

Hund's rule and metallic ferromagnetism

We study tight-binding models of itinerant electrons in two different bands, with effective on-site interactions expressing Coulomb repulsion and Hund's rule. We prove that, for sufficiently large on-site exchange anisotropy, all ground states show metallic ferromagnetism: They exhibit a macroscopic magnetization, a macroscopic fraction of the electrons is spatially delocalized, and there is no energy gap for kinetic excitations.Comment: 17 page