One Dimensional Kondo Lattice Model Studied by the Density Matrix Renormalization Group Method

Recent developments of the theoretical investigations on the one-dimensional Kondo lattice model by using the density matrix renormalization group (DMRG) method are discussed in this review. Short summaries are given for the zero-temperature DMRG, the finite-temperature DMRG, and also its application to dynamic quantities. Away from half-filling, the paramagnetic metallic state is shown to be a Tomonaga-Luttinger liquid with the large Fermi surface. For the large Fermi surface its size is determined by the sum of the densities of the conduction electrons and the localized spins. The correlation exponent K_rho of this metallic phase is smaller than 1/2. At half-filling the ground state is insulating. Excitation gaps are different depending on channels, the spin gap, the charge gap and the quasiparticle gap. Temperature dependence of the spin and charge susceptibilities and specific heat are discussed. Particularly interesting is the temperature dependence of various excitation spectra, which show unusual properties of the Kondo insulators.Comment: 18 pages, 23 Postscript figures, REVTe

Supershells in Metal Clusters: Self-Consistent Calculations and their Semiclassical Interpretation

To understand the electronic shell- and supershell-structure in large metal clusters we have performed self-consistent calculations in the homogeneous, spherical jellium model for a variety of different materials. A scaling analysis of the results reveals a surprisingly simple dependence of the supershells on the jellium density. It is shown how this can be understood in the framework of a periodic-orbit-expansion by analytically extending the well-known semiclassical treatment of a spherical cavity to more realistic potentials.Comment: 4 pages, revtex, 3 eps figures included, for additional information see http://radix2.mpi-stuttgart.mpg.de/koch/Diss

Deformed Harmonic Oscillators for Metal Clusters: Analytic Properties and Supershells

The analytic properties of Nilsson's Modified Oscillator (MO), which was first introduced in nuclear structure, and of the recently introduced, based on quantum algebraic techniques, 3-dimensional q-deformed harmonic oscillator (3-dim q-HO) with Uq(3) > SOq(3) symmetry, which is known to reproduce correctly in terms of only one parameter the magic numbers of alkali clusters up to 1500 (the expected limit of validity for theories based on the filling of electronic shells), are considered. Exact expressions for the total energy of closed shells are determined and compared among them. Furthermore, the systematics of the appearance of supershells in the spectra of the two oscillators is considered, showing that the 3-dim q-HO correctly predicts the first supershell closure in alkali clusters without use of any extra parameter.Comment: 25 pages LaTeX plus 21 postscript figure

On the 3n+l Quantum Number in the Cluster Problem

It has recently been suggested that an exactly solvable problem characterized by a new quantum number may underlie the electronic shell structure observed in the mass spectra of medium-sized sodium clusters. We investigate whether the conjectured quantum number 3n+l bears a similarity to the quantum numbers n+l and 2n+l, which characterize the hydrogen problem and the isotropic harmonic oscillator in three dimensions.Comment: 8 pages, revtex, 4 eps figures included, to be published in Phys.Rev.A, additional material available at http://radix2.mpi-stuttgart.mpg.de/koch/Diss

Periodic orbit theory for realistic cluster potentials: The leptodermous expansion

The formation of supershells observed in large metal clusters can be qualitatively understood from a periodic-orbit-expansion for a spherical cavity. To describe the changes in the supershell structure for different materials, one has, however, to go beyond that simple model. We show how periodic-orbit-expansions for realistic cluster potentials can be derived by expanding only the classical radial action around the limiting case of a spherical potential well. We give analytical results for the leptodermous expansion of Woods-Saxon potentials and show that it describes the shift of the supershells as the surface of a cluster potential gets softer. As a byproduct of our work, we find that the electronic shell and supershell structure is not affected by a lattice contraction, which might be present in small clusters.Comment: 15 pages RevTex, 11 eps figures, additional information at http://www.mpi-stuttgart.mpg.de/docs/ANDERSEN/users/koch/Diss

Orbits in Large Aluminum Clusters: Five-Pointed Stars

The distinctions in the mass spectra of large sodium (Na_N) and aluminum (Al_N) clusters are discussed. A semiclassical method is used to describe the shell effects within a spherical jellium model. It allows one to analyze the relative role of different classical trajectories in the formation of electronic supershells in clusters of various sizes at zero and finite temperatures. A criterion for the hardness of the self-consistent potential is formulated. The conjecture that the five-point-star trajectories make the main contribution to the spectral oscillations for large soft-potential Al_N (250<N<900) clusters is substantiated. The computational results are in agreement with the mass spectra of the Al_N clusters at T ~ 300 K.Comment: 5 pages, 3 figures, PDF forma