91 research outputs found
Haldane fractional statistics in the fractional quantum Hall effect
We have tested Haldane's ``fractional-Pauli-principle'' description of
excitations around the state in the FQHE, using exact results for
small systems of electrons. We find that Haldane's prediction
for quasiholes and quasiparticles, respectively, describes our results well
with the modification rather than . We also find
that this approach enables us to better understand the {\it energetics\/} of
the ``daughter'' states; in particular, we find good evidence, in terms of the
effective interaction between quasiparticles, that the states and
4/13 should not be stable.Comment: 9 pages, 3 Postscript figures, RevTex 3.0. (UCF-CM-93-005
Inferring Pattern and Disorder in Close-Packed Structures from X-ray Diffraction Studies, Part I: epsilon-Machine Spectral Reconstruction Theory
In a recent publication [D. P. Varn, G. S. Canright, and J. P. Crutchfield,
Phys. Rev. B {\bf 66}:17, 156 (2002)] we introduced a new technique for
discovering and describing planar disorder in close-packed structures (CPSs)
directly from their diffraction spectra. Here we provide the theoretical
development behind those results, adapting computational mechanics to describe
one-dimensional structure in materials. By way of contrast, we give a detailed
analysis of the current alternative approach, the fault model (FM), and offer
several criticisms. We then demonstrate that the computational mechanics
description of the stacking sequence--in the form of an
epsilon-machine--provides the minimal and unique description of the crystal,
whether ordered, disordered, or some combination. We find that we can detect
and describe any amount of disorder, as well as materials that are mixtures of
various kinds of crystalline structure. Underlying this approach is a novel
method for epsilon-machine reconstruction that uses correlation functions
estimated from diffraction spectra, rather than sequences of microscopic
configurations, as is typically used in other domains. The result is that the
methods developed here can be adapted to a wide range of experimental systems
in which spectroscopic data is available.Comment: 26 pages, 23 figures, 8 tables, 110 citations;
http://www.santafe.edu/projects/CompMech/papers/ipdcpsi.htm
Inferring Pattern and Disorder in Close-Packed Structures from X-ray Diffraction Studies, Part II: Structure and Intrinsic Computation in Zinc Sulphide
In the previous paper of this series [D. P. Varn, G. S. Canright, and J. P.
Crutchfield, Physical Review B, submitted] we detailed a
procedure--epsilon-machine spectral reconstruction--to discover and analyze
patterns and disorder in close-packed structures as revealed in x-ray
diffraction spectra. We argued that this computational mechanics approach is
more general than the current alternative theory, the fault model, and that it
provides a unique characterization of the disorder present. We demonstrated the
efficacy of computational mechanics on four prototype spectra, finding that it
was able to recover a statistical description of the underlying modular-layer
stacking using epsilon-machine representations. Here we use this procedure to
analyze structure and disorder in four previously published zinc sulphide
diffraction spectra. We selected zinc sulphide not only for the theoretical
interest this material has attracted in an effort to develop an understanding
of polytypism, but also because it displays solid-state phase transitions and
experimental data is available.Comment: 15 pages, 14 figures, 4 tables, 57 citations;
http://www.santafe.edu/projects/CompMech/papers/ipdcpsii.htm
Quantum Hall fractions for spinless Bosons
We study the Quantum Hall phases that appear in the fast rotation limit for
Bose-Einstein condensates of spinless bosonic atoms. We use exact
diagonalization in a spherical geometry to obtain low-lying states of a small
number of bosons as a function of the angular momentum. This allows to
understand or guess the physics at a given filling fraction nu, ratio of the
number of bosons to the number of vortices. This is also the filling factor of
the lowest Landau level. In addition to the well-known Bose Laughlin state at
nu =1/2 we give evidence for the Jain principal sequence of incompressible
states at nu =p/(p+- 1) for a few values of p. There is a collective mode in
these states whose phenomenology is in agreement with standard arguments coming
e.g. from the composite fermion picture. At filling factor one, the potential
Fermi sea of composite fermions is replaced by a paired state, the Moore-Read
state. This is most clearly seen from the half-flux nature of elementary
excitations. We find that the hierarchy picture does not extend up to the point
of transition towards a vortex lattice. While we cannot conclude, we
investigate the clustered Read-Rezayi states and show evidence for
incompressible states at the expected ratio of flux vs number of Bose
particles.Comment: RevTeX 4, 11 pages, 13 figure
Analytical solution for the Fermi-sea energy of two-dimensional electrons in a magnetic field: lattice path-integral approach and quantum interference
We derive an exact solution for the total kinetic energy of noninteracting
spinless electrons at half-filling in two-dimensional bipartite lattices. We
employ a conceptually novel approach that maps this problem exactly into a
Feynman-Vdovichenko lattice walker. The problem is then reduced to the analytic
study of the sum of magnetic phase factors on closed paths. We compare our
results with the ones obtained through numerical calculations.Comment: 5 pages, RevTe
"Spin-Disentangled" Exact Diagonalization of Repulsive Hubbard Systems: Superconducting Pair Propagation
By a novel exact diagonalization technique we show that bound pairs propagate
between repulsive Hubbard clusters in a superconducting fashion. The size of
the matrices that must be handled depends on the number of fermion
configurations {\em per spin}, which is of the order of the square root of the
overall size of the Hilbert space. We use CuO units connected by weak O-O
links to model interplanar coupling and c-axis superconductivity in Cuprates.
The numerical evidence on CuO and CuO prompts a new
analytic scheme describing the propagation of bound pairs and also the
superconducting flux quantization in a 3-d geometry.Comment: 5 pages, 3 figure
Exclusion statistics for fractional quantum Hall states on a sphere
We discuss exclusion statistics parameters for quasiholes and quasielectrons
excited above the fractional quantum Hall states near . We
derive the diagonal statistics parameters from the (``unprojected'') composite
fermion (CF) picture. We propose values for the off-diagonal (mutual)
statistics parameters as a simple modification of those obtained from the
unprojected CF picture, by analyzing finite system numerical spectra in the
spherical geometry.Comment: 9 pages, Revtex, 4 Postscript figures. Universality of the statistics
parameters is stressed, 2 figs adde
The Energy Density in the Maxwell-Chern-Simons Theory
A two-dimensional nonrelativistic fermion system coupled to both
electromagnetic gauge fields and Chern-Simons gauge fields is analysed.
Polarization tensors relevant in the quantum Hall effect and anyon
superconductivity are obtained as simple closed integrals and are evaluated
numerically for all momenta and frequencies. The correction to the energy
density is evaluated in the random phase approximation (RPA), by summing an
infinite series of ring diagrams. It is found that the correction has
significant dependence on the particle number density.
In the context of anyon superconductivity, the energy density relative to the
mean field value is minimized at a hole concentration per lattice plaquette
(0.05 \sim 0.06) (p_c a/\hbar)^2 where p_c and a are the momentum cutoff and
lattice constant, respectively. At the minimum the correction is about -5 %
\sim -25 %, depending on the ratio (2m \omega_c)/(p_c^2) where \omega_c is the
frequency cutoff.
In the Jain-Fradkin-Lopez picture of the fractional quantum Hall effect the
RPA correction to the energy density is very large. It diverges logarithmically
as the cutoff is removed, implying that corrections beyond RPA become important
at large momentum and frequency.Comment: 19 pages (plain Tex), 12 figures not included, UMN-TH-1246/9
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