H. Keiter

Investigation of the low temperature behaviour of the Anderson lattice

A recently developed new perturbational approach to the nonlocal correlations in the Anderson lattice model is used to study low temperature properties. These include the one particle excitation spectra and possible instabilities towards magnetic or superconducting states. The method rests upon a systematic and in principle exact incorporation of the large interaction energy, the Coulomb repulsionU between local electrons on the same lattice site, into the low energy dynamics of quasiparticles and phonons. The resulting dressing of quasiparticles and their resulting effective interactions are treated in the frame of established approximations: The former in NCA, self-consistently adapted to the lattice (LNCA), and the interacting low energy problem with help of ladder summations for the two-particle scattering. Numerical results for the one particle properties are presented, which show an interesting collective effect in the formation of a Kondo lattice state. Stoner-like expressions for various susceptibilitites are derived. Criteria for the occurrence of magnetic and different superconducting phases are given which clearly exhibit the role of quasiparticle band structure, electron-electron interaction and electronphonon interaction.

The parallel implementation of configuration‐selecting multireference configuration interaction method

We report on a scalable implementation of the configuration‐selecting multireference configuration interaction method for massively parallel architectures with distributed memory. Based on a residue driven evaluation of the matrix elements, this approach allows the routine treatment of Hilbert spaces of well over 109 determinants, as well as the selective treatment of triple and quadruple excitations with respect to the reference space. We demonstrate the scalability of the method for up to 128 nodes on the IBM‐SP2 and for up to 256 nodes on the Cray‐T3E. We elaborate on the specific adaptation of the transition residue‐based matrix element evaluation scheme that ensures the scalability and load balancing of the method. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1559–1570, 1999

Large-N-limit of mixed valence: Diagrammatic expansion and rigorous results

For an intermediate valence model, containing one simply and oneN-fold degeneratef-configuration at a specific lattice site, the large-N-limit is studied within a concise diagrammatic expansion and also rigorously. At zero temperatureT rigorous upper and lower bounds for the ground state energy are found, while at finiteT the large-N-expansion is shown to be equivalent to the principle of classifying the diagrams according the maximum number of spin flips, whereupon various physical quantities can be calculated.

On Suhl's dispersion equations for dilute magnetic alloys in a finite magnetic field

The system of six coupled, nonlinear, singular integral equations, devised by Suhl to treat the problem of a spin 1/2 magnetic impurity in a finite magnetic field is shown to be reducible to a single integral equation. Analytic properties and symmetries of the system are discussed, which may serve as a guideline for numerical studies of the final integral equation. The first few steps of an iteration in terms of the magnetic field strength are carried out analytically.

On the zero-bandwidth limit in diagrammatic perturbation technique for a model of an intermediate valent impurity

The limit of zero bandwidth in a model for an intermediate valent impurity is studied in direct diagrammatic perturbation technique in terms of the hybridization. The class of diagrams, from which this limit is obtained, is resummed. Furthermore, a Brillouin-Wigner-type expansion is set up.

Dynamic properties of the anderson model at finiteU

TheN-fold-degenerate single impurity Anderson model is studied at finiteU, using the perturbation expansion in the hybridizationV. The 1/N-expansion and the energy-dependence of the self-energies allow to set up a system of self-consistent integral equations for the self-energies, and thef-spectral function. Thef-spectral density and transport coefficients (the electrical resistivity ρ, the Lorenz ratioL/L0, the thermoelectric powerS, and the Hall-coefficientRH) are calculated numerically via the self-consistent integral equations. We are particularly interested in the effect of the Coulomb interaction on the dynamic properties. Thef-spectral function is calculated at small and largeU. It shows a sharp peak at the Fermilevel (the Kondo-Abrikosov-Suhl resonance) and two broad peaks around εf and εf+U. The structure at the Fermi-level is very sensitive to the Coulomb interactionU. In order to get more information about the model, we have studied the transport coefficients at differentU, which are universal functions of the temperatureT/TK, where the Kondo-temperature sets the scale. We find that the transport coefficients show Kondo behavior aroundT≅TK, and are also sensitive toU. The Hall-coefficient is negative forT≦TK already within the impurity model. This competes with the usual interpretation as a coherence effect caused by the lattice.

Systematic perturbation calculation for a non commutative model for a metallic glas

We present a systematic perturbation calculation up to the 4th order in the interaction for a metallic-glas-model with an anisotropic coupling of the conduction electrons to a local two-level-system. The logarithmic-(infrared-)divergent terms for the electronic lifetime are suppressed by exponentially small prefactors in the region I (E≫ω≫T) whereas in the region II (E≪ω≪T) they survive in the general case of non-commuting elastic and inelastic couplings in the Hamiltonian, whereE denotes the level-splittings of the local-system, ω the excitation energy of the conduction electrons above the Fermi level, andT the thermal energy.

Comment on many-body aspects of external photoemission

It is emphasized that the relation between the Laplace-transformed three-current-operator retarded commutator Greens function occurring in quadratic response theory of external photoemission, and the three-current temperature Greens function permits a standard many-body analysis of photoemission. As an example, a diagrammatic particlehole analysis yields generalized golden-rule formulae at finite temperature. Also, conserving approximations can be formally set up quite easily in the framework of the Kadanoff-Baym formalism, yielding quadratic response to the total field inside the specimen, thus limiting the “volume effect”.

Multiparticle entanglement and ranks of density matrices

Based on the ranks of reduced density matrices, we derive necessary conditions for the separability of multiparticle arbitrary-dimensional mixed states, which are equivalent to sufficient conditions for entanglement. In a similar way we obtain necessary conditions for the separability of a given mixed state with respect to partitions of all particles of the system into subsets. The special case of pure states is discussed separately.

Model calculations for electronic densities of states in heavy-fermion systems

The influence of the lattice on the density of states for conduction-band andf-electrons in heavy fermion and mixed valent systems has been calculated from an extension of the non-crossing approximation to the lattice. It is shown that the main features of such a calculation can be obtained by a simple numerical simulation.