Exact diagonalization solver for the extended dynamical mean-field theory

We present an efficient exact diagonalization scheme for the extended dynamical mean-field theory and apply it to the extended Hubbard model on the square lattice with nonlocal charge-charge interactions. Our solver reproduces the phase diagram of this approximation with good accuracy. Details on the numerical treatment of the large Hilbert space of the auxiliary Holstein-Anderson impurity problem are provided. Benchmarks with a numerically exact strong-coupling continuous-time quantum-Monte Carlo solver show better convergence behavior of the exact diagonalization in the deep insulator. Special attention is given to possible effects due to the discretization of the bosonic bath. We discuss the quality of real axis spectra and address the question of screening in the Mott insulator within extended dynamical mean-field theory.Comment: 12 pages, 8 figure

Effective Heisenberg model and exchange interaction for strongly correlated systems

We consider the extended Hubbard model and introduce a corresponding Heisenberg-like problem written in terms of spin operators. The derived formalism is reminiscent of Anderson's idea of the effective exchange interaction and takes into account nonlocal correlation effects. The results for the exchange interaction and magnetic susceptibility are expressed in terms of single-particle quantities, which can be obtained efficiently in realistic calculations of multiband systems. In the strongly spin-polarized limit, when the local magnetic moment is well-defined, the exchange interaction reduces to a standard expression of the density functional theory that has been successfully used in practical calculations of magnetic properties of real materials.Comment: Accepted to Physical Review Letter

Conservation in two-particle self-consistent extensions of dynamical-mean-field-theory

Extensions of dynamical-mean-field-theory (DMFT) make use of quantum impurity models as non-perturbative and exactly solvable reference systems which are essential to treat the strong electronic correlations. Through the introduction of retarded interactions on the impurity, these approximations can be made two-particle self-consistent. This is of interest for the Hubbard model, because it allows to suppress the antiferromagnetic phase transition in two-dimensions in accordance with the Mermin-Wagner theorem, and to include the effects of bosonic fluctuations. For a physically sound description of the latter, the approximation should be conserving. In this paper we show that the mutual requirements of two-particle self-consistency and conservation lead to fundamental problems. For an approximation that is two-particle self-consistent in the charge- and longitudinal spin channel, the double occupancy of the lattice and the impurity are no longer consistent when computed from single-particle properties. For the case of self-consistency in the charge- and longitudinal as well as transversal spin channels, these requirements are even mutually exclusive so that no conserving approximation can exist. We illustrate these findings for a two-particle self-consistent and conserving DMFT approximation.Comment: 17 pages, 9 figure

Die Evaluations-Matrix: Ein Tool zur Bewertung antriebs- und kraftstoff-technologischer Innovationen in der Automobilindustrie

Das Automobil ist nicht nur mit Abstand der Verkehrsträger Nummer 1, sondern es ist ein integraler Bestandteil moderner Gesellschaften und ein Symbol für Status, Wohlstand, Freiheit, Dynamik und Fortschritt. Der harte technische Kern des Autos besteht in einer über hundert Jahre alten Verbrennungsmotorik, bei der fossile Brennstoffe aus der Natur importiert und Treibhausgase in die Natur exportiert werden. Dieser harte technische Kern erweist sich zunehmend als problematisch, und zwar sowohl im Hinblick auf die Verfügbarkeit von fossilen Brennstoffen als auch in Bezug auf die Emissionen und deren Folgen. Im letzten Jahrzehnt wurde deshalb weltweit eine Vielzahl von Innovationen in Angriff genommen, um die fossile Verbrennungsmotorik zu optimieren und zu substituieren. In der vorliegenden Arbeit wird der Versuch unternommen, dieses breit gefächerte Feld antriebs- und kraftstofftechnologischer Innovationen aus einer interdisziplinären Perspektive zu systematisieren und zu evaluieren. Im Zentrum steht dabei die Entwicklung einer Evaluations- Matrix. Mit dieser Matrix werden zwei Ziele verfolgt. Erstens sollen die Innovationen mit Hilfe technischer, ökonomischer und ökologischer Parameter quantifiziert werden. Aufbauend darauf werden diese Innovationen dann zweitens im Hinblick auf die Erreichung gesetzlicher Zielvorgaben miteinander verglichen und bewertet. -- Not only is the automobile the world's number one transportation vehicle, it is also a vital part of modern societies. It is a status symbol representing prosperity, freedom, and progress. The main technical component of the automobile is the more than a century old internal combustion engine which, in order to function, requires fossil fuels. Despite this dependency on nature, the toxic gases it produces are responsible for an important part of the pollution to our environment. Thus the internal combustion engine is increasingly becoming a problem due to the limitation of the fossil fuels it requires, on the one hand, and to the toxic emissions and subsequent environmental pollution it produces on the other. For the past decade, a multitude of technical innovations has been presented and implemented worldwide in order to optimize or even provide a substitute for the internal combustion engine. It is the purpose of this paper to attempt to analyse this wide variety of innovations in the fields of alternative fuels and new engine types from an interdisciplinary perspective. This analysis is centred around the development of an evaluation matrix. This matrix has two aims, the first of which is to quantify these innovations by using technical, economical and ecological parameters. Based on these parameters, the innovations are then compared and evaluated with regard to meeting the statutory objectives.