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

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

Rough droplet model for spherical metal clusters

We study the thermally activated oscillations, or capillary waves, of a neutral metal cluster within the liquid drop model. These deformations correspond to a surface roughness which we characterize by a single parameter $\Delta$. We derive a simple analytic approximate expression determining $\Delta$ as a function of temperature and cluster size. We then estimate the induced effects on shell structure by means of a periodic orbit analysis and compare with recent data for shell energy of sodium clusters in the size range $50 < N < 250$. A small surface roughness $\Delta\simeq 0.6$ \AA~ is seen to give a reasonable account of the decrease of amplitude of the shell structure observed in experiment. Moreover -- contrary to usual Jahn-Teller type of deformations -- roughness correctly reproduces the shape of the shell energy in the domain of sizes considered in experiment.Comment: 20 pages, 4 figures, important modifications of the presentation, to appear in Phys. Rev.

Un ancien recteur de l’Académie de Paris : Adolphe Mourier

Cosme Léon. Un ancien recteur de l’Académie de Paris : Adolphe Mourier. In: Revue internationale de l'enseignement, tome 48, Juillet-Décembre 1904. pp. 221-227