9 research outputs found
The numerical renormalization group method for quantum impurity systems
In the beginning of the 1970's, Wilson developed the concept of a fully
non-perturbative renormalization group transformation. Applied to the Kondo
problem, this numerical renormalization group method (NRG) gave for the first
time the full crossover from the high-temperature phase of a free spin to the
low-temperature phase of a completely screened spin. The NRG has been later
generalized to a variety of quantum impurity problems. The purpose of this
review is to give a brief introduction to the NRG method including some
guidelines of how to calculate physical quantities, and to survey the
development of the NRG method and its various applications over the last 30
years. These applications include variants of the original Kondo problem such
as the non-Fermi liquid behavior in the two-channel Kondo model, dissipative
quantum systems such as the spin-boson model, and lattice systems in the
framework of the dynamical mean field theory.Comment: 55 pages, 27 figures, submitted to Rev. Mod. Phy
Phase diagram of UPt in the model
The phase diagram of the unconventional superconductor UPt is explained
under the long-standing hypothesis that the pair wavefunction belongs to the
representation of the point group. The main objection to this theory
has been that it disagrees with the experimental phase diagram when a field is
applied along the c-axis. By a careful analysis of the free energy this
objection is shown to be incorrect. This singlet theory also explains the
unusual anisotropy in the upper critical field curves, often thought to
indicate a triplet pair function.Comment: 11 pages, Revtex, 2 figures (uuencoded, gzip'ed Postscript
Quadrupolar interactions in Pr compounds: PrFe4P12 and PrBa2Cu3O6
We examine trivalent Pr crystal field models with near-degeneracy of the two
lowest crystal field levels, where interaction-induced quadrupolar and dipolar
moments are as important as the permanent moments of the crystal field ground
state. We find that the Gamma1-Gamma4 level scheme yields a successful
description of the antiferroquadrupolar ordering of PrFe4P12. For PrBa2Cu3O6,
we argue that quadrupolar interaction is important for understanding the Pr
ordering transition at 11K.Comment: One of the figures, and a few sentences replaced. 8 pages, 5 figures,
iopart submitted to the Proceedings of the conference on "Advances in the
Physics of f-electron Systems (JAERI Tokai, Japan), accepted for publication
in J. Phys.: Condensed Matte
model of superconducting UPt
The phase diagram of superconducting UPt is explained in a
Ginzburg-Landau theory starting from the hypothesis that the order parameter is
a pseudo-spin singlet which transforms according to the representation
of the point group. We show how to compute the positions of the phase
boundaries both when the applied field is in the basal plane and when it is
along the c-axis. The experimental phase diagrams as determined by longitudinal
sound velocity data can be fit using a single set of parameters. In particular
the crossing of the upper critical field curves for the two field directions
and the apparent isotropy of the phase diagram are reproduced. The former is a
result of the magnetic properties of UPt and their contribution to the free
energy in the superconducting state. The latter is a consequence of an
approximate particle-hole symmetry. Finally we extend the theory to finite
pressure and show that, in contrast to other models, the model
explains the observed pressure dependence of the phase boundaries.Comment: RevTex, 29 pages, 18 PostScript figures in a uuencoded, gzipped tar
file. PostScript version of paper, tar file of PostScript figures and
individual PostScript figures are also available via anonymous ftp at
ftp://nym.physics.wisc.edu/anonymou/papers/upt3
Renormalization-group calculation of dynamical properties for impurity models
The numerical renormalization-group method was originally developed to calculate the thermodynamical properties of impurity Hamiltonians. A recently proposed generalization capable of computing dynamical properties is discussed. As illustrative applications, essentially exact results for the impurity specttral densities of the spin-degenerate Anderson model and of a model for electronic tunneling between two centers in a metal are presented. © 1991