3,524 research outputs found
Convergent expansions for properties of the Heisenberg model for CaVO
We have carried out a wide range of calculations for the Heisenberg
model with nearest- and second-neighbor interactions on a two-dimensional
lattice which describes the geometry of the vanadium ions in the spin-gap
system CaVO. The methods used were convergent high-order perturbation
expansions (``Ising'' and ``Plaquette'' expansions at , as well as
high-temperature expansions) for quantities such as the uniform susceptibility,
sublattice magnetization, and triplet elementary excitation spectrum.
Comparison with the data for CaVO indicates that its magnetic
properties are well described by nearest-neighbor exchange of about 200K in
conjunction with second-neighbor exchange of about 100K.Comment: Uses REVTEX macros. Four pages in two-column format, five postscript
figures. Files packaged using uufile
The twistor geometry of three-qubit entanglement
A geometrical description of three qubit entanglement is given. A part of the
transformations corresponding to stochastic local operations and classical
communication on the qubits is regarded as a gauge degree of freedom. Entangled
states can be represented by the points of the Klein quadric a space
known from twistor theory. It is shown that three-qubit invariants are
vanishing on special subspaces of . An invariant vanishing for the
class is proposed. A geometric interpretation of the canonical
decomposition and the inequality for distributed entanglement is also given.Comment: 4 pages RevTeX
Zero Curvature Formalism for Supersymmetric Integrable Hierarchies in Superspace
We generalize the Drinfeld-Sokolov formalism of bosonic integrable
hierarchies to superspace, in a way which systematically leads to the zero
curvature formulation for the supersymmetric integrable systems starting from
the Lax equation in superspace. We use the method of symmetric space as well as
the non-Abelian gauge technique to obtain the supersymmetric integrable
hierarchies of the AKNS type from the zero curvature condition in superspace
with the graded algebras, sl(n+1,n), providing the Hermitian symmetric space
structure.Comment: LaTeX, 9 pg
Darboux transformations for a twisted derivation and quasideterminant solutions to the super KdV equation
This paper is concerned with a generalized type of Darboux transformations
defined in terms of a twisted derivation satisfying
where is a homomorphism. Such twisted derivations include regular
derivations, difference and -difference operators and superderivatives as
special cases. Remarkably, the formulae for the iteration of Darboux
transformations are identical with those in the standard case of a regular
derivation and are expressed in terms of quasideterminants. As an example, we
revisit the Darboux transformations for the Manin-Radul super KdV equation,
studied in Q.P. Liu and M. Ma\~nas, Physics Letters B \textbf{396} 133--140,
(1997). The new approach we take enables us to derive a unified expression for
solution formulae in terms of quasideterminants, covering all cases at once,
rather than using several subcases. Then, by using a known relationship between
quasideterminants and superdeterminants, we obtain expressions for these
solutions as ratios of superdeterminants. This coincides with the results of
Liu and Ma\~nas in all the cases they considered but also deals with the one
subcase in which they did not obtain such an expression. Finally, we obtain
another type of quasideterminant solutions to the Main-Radul super KdV equation
constructed from its binary Darboux transformations. These can also be
expressed as ratios of superdeterminants and are a substantial generalization
of the solutions constructed using binary Darboux transformations in earlier
work on this topic
Spin-S bilayer Heisenberg models: Mean-field arguments and numerical calculations
Spin-S bilayer Heisenberg models (nearest-neighbor square lattice
antiferromagnets in each layer, with antiferromagnetic interlayer couplings)
are treated using dimer mean-field theory for general S and high-order
expansions about the dimer limit for S=1, 3/2,...,4. We suggest that the
transition between the dimer phase at weak intraplane coupling and the Neel
phase at strong intraplane coupling is continuous for all S, contrary to a
recent suggestion based on Schwinger boson mean-field theory. We also present
results for S=1 layers based on expansions about the Ising limit: In every
respect the S=1 bilayers appear to behave like S=1/2 bilayers, further
supporting our picture for the nature of the order-disorder phase transition.Comment: 6 pages, Revtex 3.0, 8 figures (not embedded in text
Effective-Medium Theory for the Normal State in Orientationally Disordered Fullerides
An effective-medium theory for studying the electronic structure of the
orientationally disordered A3C60 fullerides is developed and applied to study
various normal-state properties. The theory is based on a cluster-Bethe-lattice
method in which the disordered medium is modelled by a three-band Bethe
lattice, into which we embed a molecular cluster whose scattering properties
are treated exactly. Various single-particle properties and the
frequency-dependent conductivity are calculated in this model, and comparison
is made with numerical calculations for disordered lattices, and with
experiment.Comment: 12 pages + 2 figures, REVTeX 3.
Coupling Poisson and Jacobi structures on foliated manifolds
Let M be a differentiable manifold endowed with a foliation F. A Poisson
structure P on M is F-coupling if the image of the annihilator of TF by the
sharp-morphism defined by P is a normal bundle of the foliation F. This notion
extends Sternberg's coupling symplectic form of a particle in a Yang-Mills
field. In the present paper we extend Vorobiev's theory of coupling Poisson
structures from fiber bundles to foliations and give simpler proofs of
Vorobiev's existence and equivalence theorems of coupling Poisson structures on
duals of kernels of transitive Lie algebroids over symplectic manifolds. Then
we discuss the extension of the coupling condition to Jacobi structures on
foliated manifolds.Comment: LateX, 38 page
Ground State and Elementary Excitations of the S=1 Kagome Heisenberg Antiferromagnet
Low energy spectrum of the S=1 kagom\'e Heisenberg antiferromagnet (KHAF) is
studied by means of exact diagonalization and the cluster expansion. The
magnitude of the energy gap of the magnetic excitation is consistent with the
recent experimental observation for \mpynn. In contrast to the KHAF,
the non-magnetic excitations have finite energy gap comparable to the magnetic
excitation. As a physical picture of the ground state, the hexagon singlet
solid state is proposed and verified by variational analysis.Comment: 5 pages, 7 eps figures, 2 tables, Fig. 4 correcte
Recursion relations and branching rules for simple Lie algebras
The branching rules between simple Lie algebras and its regular (maximal)
simple subalgebras are studied. Two types of recursion relations for anomalous
relative multiplicities are obtained. One of them is proved to be the
factorized version of the other. The factorization property is based on the
existence of the set of weights specific for each injection. The
structure of is easily deduced from the correspondence between the
root systems of algebra and subalgebra. The recursion relations thus obtained
give rise to simple and effective algorithm for branching rules. The details
are exposed by performing the explicit decomposition procedure for injection.Comment: 15p.,LaTe
Dispersion for the Schr\"odinger Equation on Networks
In this paper we consider the Schr\"odinger equation on a network formed by a
tree with the last generation of edges formed by infinite strips. We give an
explicit description of the solution of the linear Schr\"odinger equation with
constant coefficients. This allows us to prove dispersive estimates, which in
turn are useful for solving the nonlinear Schr\"odinger equation. The proof
extends also to the laminar case of positive step-function coefficients having
a finite number of discontinuities.Comment: 16 pages, 2 figure
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