N. Grewe

Spectral properties of the Anderson model

An investigation of the one particle spectrum of the (impurity-) Anderson model within the time ordered perturbation approach is presented. The approximation used includes all processes without crossing band electron lines and does not make use of the Brillouin-Wigner scheme. Foregoing treatments are thus generalized in essential points. Local self energies are determined by two coupled integral equations which are solved numerically. Numerical procedures and the validity of the approximation are thoroughly tested for the resonant level model, which deals with only one spin component and is exactly solvable. Calculated spectra for the Anderson model in all regimes of temperature and of local level position are discussed. A remarkable improvement over earlier attempts is found. Connection to the resonant level model is made by analytical continuation in the number of spin components. The approximation is placed into a general context of a conserved skeleton diagram expansion. It is pointed out how it can systematically be improved, and some exact formulas are derived.

Perturbation expansions for systems with strong local correlation

Systems with two kinds of electrons, one localized and strongly correlated, the other in extended band states, require unconventional perturbational concepts. The application of time ordered perturbation expansions with respect to hybridization is studied. The Brillouin-Wigner scheme is critically investigated and a more general method developed. Particular care is devoted to a discussion of summation methods for diagrams in infinite order, and a new set of integral equations is derived. These avoid explicit regularization procedures and lend themselves naturally to investigations of the Kondo-and Intermediate Valence-regimes. Some general expressions for partition fuction and local Greens function of the impurity problem are studied and related to theT-matrix of compounds. Two exactly solvable cases, the resonant level model and the limit of zero bandwidth, serve as examples and guides for approximations.

Lattice dynamics in mixed valent Rare Earth compounds

In the frame of a single coherent picture for the electron lattice interactions in mixed valent Rare Earth compounds, the phase diagrams and phonon dispersions are studied. Our model is introduced on a microscopic level and discussed in detail. The mechanism of the phase transition and the role of the lattice is illuminated and various properties are considered in a model calculation. Anomalies in the phonon dispersions of Sm1−xYxS, which have recently been found, find a satisfying explanation.

Mixed valencies: Structure of phase diagrams, lattice properties and the consequences of electron hole symmetry

AbstractSymmetry properties and phonon phenomena of mixed valence compounds are discussed within the framework of the periodic Anderson model which was extended to include the interaction of 4f electrons with longitudinal optical phonons. The temperature anomaly in the thermal expansion found in CeSn3 (positive thermal expansion coefficientα) and YbCuAl (negativeα) is correctly described. Within the model the anomaly is a consequence of the particle hole symmetry of the underlying Hamiltonian. Moreover, the theory gives the positive slope of the phase boundary in the pressure-temperature phase diagram (dP/dT>0), for example for Ce, and predicts a negative slope (dP/dT<0) for Yb compounds.Furthermore, the quite unusual low temperature features of the pressure-temperature phase diagram have been calculated. It is found that the lattice vibrational contribution renormalizes the two essential parameters of the periodic Anderson model. The hybridization energyV0 of 4f and 5d−6s states is changed to

Phonon induced instabilities in intermediate valence compounds

\tilde V

Unusual critical behaviour of ferromagnetic superconductors

=V0−aφ−b〈ϕ2〉 whereas the energy of the 4f stateE0 with respect to the 5d band becomes

Scaling approach to the theory of frequency dependent hopping conductivity of disordered systems

\tilde E