Plasmons in strongly correlated systems: spectral weight transfer and renormalized dispersion.

We study the charge-density dynamics within the two-dimensional extended Hubbard model in the presence of long-range Coulomb interaction across the metal-insulator transition point. To take into account strong correlations we start from self-consistent extended dynamical mean-field theory and include nonlocal dynamical vertex corrections through a ladder approximation to the polarization operator. This is necessary to fulfill charge conservation and to describe plasmons in the correlated state. The calculated plasmon spectra are qualitatively different from those in the random-phase approximation: they exhibit a spectral density transfer and a renormalized dispersion with enhanced deviation from the canonical √q behavior. Both features are reminiscent of interaction induced changes found in single-electron spectra of strongly correlated systems.

Efficient perturbation theory for quantum lattice models.

We present a novel approach to long-range correlations beyond dynamical mean-field theory, through a ladder approximation to dual fermions. The new technique is applied to the two-dimensional Hubbard model. We demonstrate that the transformed perturbation series for the nonlocal dual fermions has superior convergence properties over standard diagrammatic techniques. The critical Néel temperature of the mean-field solution is suppressed in the ladder approximation, in accordance with quantum Monte Carlo results. An illustration of how the approach captures and allows us to distinguish short- and long-range correlations is given.

Understanding the electronic structure and magnetism of correlated nanosystems.

In this paper we review recent developments towards a realistic description of the electronic structure and magnetism of correlated nanosystems. A new class of so-called continuous-time solvers for the quantum impurity problem is discussed, which provides a numerically exact solution without systematic errors due to imaginary time discretization. These solvers are able to handle general interactions, like the full Coulomb vertex. We further show how four-point or higher-order correlation functions of the impurity problem can be computed. This allows the calculation of dynamical susceptibilities which provide information about spin excitations. Moreover, we discuss a principally new many-body scheme recently proposed for the description of non-local correlations in strongly correlated systems. This approach provides a basis for a many-body description of extended correlated nanostructures on a substrate.