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Dynamical mean field theory is one of the key methods to describe electronic properties of strongly correlated materials. If exact diagonalization is used as impurity solver, the size of the finite bath representing the infinite lattice is limited because of the rapid growth of the Hilbert space. In view of the increasing interest in the effect of multiorbital and multisite Coulomb correlations in transition metal oxides, highTc cuprates, ironbased pnictides, organic crystals, etc., it is appropriate to explore the range of temperatures and bath sizes in which exact diagonalization provides accurate results for various system properties. On the one hand, the bath must be large enough to achieve a sufficiently dense level spacing, so that useful spectral information can be derived, especially close to the Fermilevel. On the other hand, for an adequate projection of the lattice Green's function onto a finite bath, the choice of the temperature is crucial. The role of these two key ingredients in exact diagonalization DMFT is discussed for a wide variety of systems in order to establish the domain of applicability of this approach. Three criteria are used to illustrate the accuracy of the results: (i) the convergence of the selfenergy with bath size, (ii) quality of the discretization of the bath Green's function, and (iii) comparisons with complementary results obtained via continuoustime quantum Monte Carlo DMFT. The materials comprise a variety of multiorbital systems, as well as singleband Hubbard models for twodimensional triangular, square and honeycomb lattices, where nonlocal Coulomb correlations are important. The main conclusion from these examples is that a larger number of correlated orbitals or sites requires a smaller number of bath levels. Down to temperatures of 5 to 10 meV two bath levels per correlated impurity orbital or site are usually adequate.
(A. Liebsch, H. Ishida) Topical Review: J. Phys. CM 24, 053201 (2012)
The role of nonlocal Coulomb correlations in the honeycomb lattice is investigated within cluster dynamical mean field theory combined with finitetemperature exact diagonalization. The paramagnetic semimetaltoinsulator transition is found to be in excellent agreement with finitesize determinantal quantum Monte Carlo simulations and with cluster dynamical mean field calculations based on the continuoustime quantum Monte Carlo approach. As expected, the critical Coulomb energy is much lower than within a local or singlesite formulation. Shortrange correlations are shown to give rise to a pseudogap and concomitant nonFermiliquid behavior within a narrow range below the Mott transition.
(A. Liebsch) Phys. Rev. B 83, 035113 (2011)
The discovery of superconductivity in iron pnictides has stimulated intense discussions concerning the role of correlation effects, in particular, the importance of Hund exchange interactions. Optical data reveal a highenergy pseudogap not compatible with normal metal behavior. This pseudogap differs fundamentally from the lowenergy gap in the antiferromagnetic spindensity wave phase. To analyze the effect of Hund coupling, the degenerate fiveband Hubbard model is studied within dynamical mean field theory combined with exact diagonalization. A significant depletion of spectral weight is found above the Fermi level. It is shown that this pseudogap is associated with a collective mode in the selfenergy caused by spin fluctuations. The pseudogap is remarkably stable over a wide range of Coulomb and exchange energies, but disappears for weak Hund coupling.
(A. Liebsch) Phys. Rev. B 84, 180505 (2011) (Rapid Communication)
The electronic structure of small Hubbard molecules coupled between two noninteracting semiinfinite leads is studied in the low biasvoltage limit. To calculate the finitetemperature Green's function of the system, each semiinfinite lead is simulated by a small cluster, so that the problem is reduced to that of a finitesize system comprising the molecule and clusters on both sides. The Hamiltonian parameters of the cluster is chosen such that its embedding potential coincides with those of the semiinfinite leads on Matsubara points. Exact diagonalization based on the Arnoldi approach is used to evaluate the effect of Coulomb correlations on the electronic properties of the molecule at finite temperature. Depending on important Hamiltonian parameters, such as Coulomb repulsion and oneelectron hopping within the molecule, and hybridization between molecule and leads, the selfenergy of the molecule is shown to exhibit standard Fermiliquid behavior or nonFermiliquidlike deviations giving rise to finite electronic scattering rates. The present method can also describe the formation of Kondo resonances inside correlationinduced pseudogaps, as far as the associated Kondo temperature is comparable with the temperature range studied by the exact diagonalization, whose lower boundary can be reduced by increasing the cluster size. These results demonstrate how the system can be tuned between the ballistic transport regime, the Coulomb blockade regime, and the Kondo regime.
(H. Ishida, A. Liebsch) Rhys. Rev. B 86, xxx (2012)
Besides ground state properties, it is possible nowadays to grasp information on the magnetic excitations of nanostructures (adatoms, clusters and thin films) with state of the art inelastic scanning tunneling spectroscopy or electron energy loss spectroscopy. The theoretical investigation of these excitations hinges on the ability to access quantum mechanical processes behind the dynamics of a system. We use time dependent density functional theory combined with the KorringaKohnRostoker Green function method to devise a realspace scheme that enables the description of the main characteristics of magnetic excitations, i.e. their resonance frequency, their lifetime and their behavior upon application of external perturbations.
More details: Funsilab
In the endeavor for an ab initio understanding of the electronic structures of complex physical systems, double and charge transfer excitations are both receiving increasing attention due to their possible technological relevance. The former are involved in many ultrafast processes which are now experimentally accessible while the latter are believed to be essential in explaining complex processes involved in photosynthesis. The challenges to describe double and chargetransfer excitations within a densityfunctional framework are related since both require a functional which is nonlocal in space and time. Especially the nonlocality in time, i.e. a frequency
dependence, is missing from currently available functionals.
We want to develop a frequencydependent density functional which will enable us to describe both double and chargetransfer excitations. Moreover, as an alternative approach we will employ reduced densitymatrix functional theory, which has proven to be capable of solving many longstanding problems in densityfunctional theory. We will provide a stringent derivation of a time dependent version of reduced densitymatrix functional theory and derive a functional of the density matrix appropriate for the description of chargetransfer and double excitations. The properties of all functionals will be derived from exact calculations for one and twodimensional model systems where the interacting Schrödinger equation can be solved without approximations for a small number of particles.
While densityfunctional theory is an efficient groundstate scheme, manybody perturbation theory gives access to excited states and is thus the method of choice to calculate accurate excitation energies and spectroscopic functions. It is based on Green function techniques and an expansion of correlation functions in terms of Feynman diagrams. The most important practical realization is the GW approximation for the electronic selfenergy, which significantly improves the description of quasiparticle band structures, but it can equally be used to study magnon resonances in the spin susceptibility. Our implementation in the program SPEX is based on the fullpotential linearized augmented planewave (FLAPW) approach, along with FLEUR. The contribution from core electrons, the spin polarization of magnetic materials, as well as relativistic effects including spinorbit coupling can be taken into account.