21 research outputs found
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