4,166 research outputs found
GAPS IN THE HEISENBERG-ISING MODEL
We report on the closing of gaps in the ground state of the critical
Heisenberg-Ising chain at momentum . For half-filling, the gap closes at
special values of the anisotropy , integer. We explain
this behavior with the help of the Bethe Ansatz and show that the gap scales as
a power of the system size with variable exponent depending on . We use
a finite-size analysis to calculate this exponent in the critical region,
supplemented by perturbation theory at . For rational
fillings, the gap is shown to be closed for {\em all} values of and
the corresponding perturbation expansion in shows a remarkable
cancellation of various diagrams.Comment: 12 RevTeX pages + 4 figures upon reques
A Note on Dressed S-Matrices in Models with Long-Range Interactions
The {\sl dressed} Scattering matrix describing scattering of quasiparticles
in various models with long-range interactions is evaluated by means of
Korepin's method\upref vek1/. For models with -interactions
the S-matrix is found to be a momentum-independent phase, which clearly
demonstrates the ideal gas character of the quasiparticles in such models. We
then determine S-matrices for some models with -interaction
and find them to be in general nontrivial. For the -limit of the
-interaction we recover trivial S-matrices, thus exhibiting
a crossover from interacting to noninteracting quasiparticles. The relation of
the S-matrix to fractional statistics is discussed.Comment: 18 pages, jyTeX (macro included - just TeX the file) BONN-TH-94-13,
revised version: analysis of models with 1/sinh^2 interaction adde
Exact Solution of Heisenberg-liquid models with long-range coupling
We present the exact solution of two Heisenberg-liquid models of particles
with arbitrary spin interacting via a hyperbolic long-range potential. In
one model the spin-spin coupling has the simple antiferromagnetic Heisenberg
exchange form, while for the other model the interaction is of the
ferromagnetic Babujian-Takhatajan type. It is found that the Bethe ansatz
equations of these models have a similar structure to that of the
Babujian-Takhatajan spin chain. We also conjecture the integrability of a third
new spin-lattice model with long-range interaction.Comment: 7pages Revte
Long Range Interaction Models and Yangian Symmetry
The generalized Sutherland-Romer models and Yan models with internal spin
degrees are formulated in terms of the Polychronakos' approach and RTT relation
associated to the Yang-Baxter equation in consistent way. The Yangian symmetry
is shown to generate both models. We finally introduce the reflection algebra
K(u) to the long range models.Comment: 13 pages, preprint of Nankai Institute of Mathematics ( Theoretical
Physics Division ), published in Physical Review E of 1995. For hard copy,
write to Prof. Mo-lin GE directly. Do not send emails to this accoun
Self-similarity and novel sample-length-dependence of conductance in quasiperiodic lateral magnetic superlattices
We study the transport of electrons in a Fibonacci magnetic superlattice
produced on a two-dimensional electron gas modulated by parallel magnetic field
stripes arranged in a Fibonacci sequence. Both the transmission coefficient and
conductance exhibit self-similarity and the six-circle property. The presence
of extended states yields a finite conductivity at infinite length, that may be
detected as an abrupt change in the conductance as the Fermi energy is varied,
much as a metal-insulator transition. This is a unique feature of transport in
this new kind of structure, arising from its inherent two-dimensional nature.Comment: 9 pages, 5 figures, revtex, important revisions made. to be published
in Phys. Rev.
Jack polynomials with prescribed symmetry and hole propagator of spin Calogero-Sutherland model
We study the hole propagator of the Calogero-Sutherland model with SU(2)
internal symmetry. We obtain the exact expression for arbitrary non-negative
integer coupling parameter and prove the conjecture proposed by one of
the authors. Our method is based on the theory of the Jack polynomials with a
prescribed symmetry.Comment: 12 pages, REVTEX, 1 eps figur
Collective Field Description of Spin Calogero-Sutherland Models
Using the collective field technique, we give the description of the spin
Calogero-Sutherland Model (CSM) in terms of free bosons. This approach can be
applicable for arbitrary coupling constant and provides the bosonized
Hamiltonian of the spin CSM. The boson Fock space can be identified with the
Hilbert space of the spin CSM in the large limit. We show that the
eigenstates corresponding to the Young diagram with a single row or column are
represented by the vertex operators. We also derive a dual description of the
Hamiltonian and comment on the construction of the general eigenstates.Comment: 14 pages, one figure, LaTeX, with minor correction
Integrability and coherence of hopping between 1D correlated electrons systems
We present numerical evidence that the hopping of electrons between chains
described by the model is coherent in the integrable cases ( and
) and essentially incoherent otherwise. This effect is {\it not} related
to the value of the exponent , (which is restricted to the interval
[0,1/8] when ), and we propose that enhanced coherence is
characteristic of integrable systems.Comment: 9 pages, LateX, 4 figures in uuencoded format, submitted to Phys.
Rev. Let
Bosonization of current-current interactions
We discuss a generalization of the conventional bosonization procedure to the
case of current-current interactions which get their natural representation in
terms of current instead of fermion number density operators. A consistent
bosonization procedure requires a geometrical quantization of the hamiltonian
action of on its coadjoint orbits. An integrable example of a
nontrivial realization of this symmetry is presented by the Calogero-Sutherland
model. For an illustrative nonintegrable example we consider transverse gauge
interactions and calculate the fermion Green function.Comment: 15 pages, TeX, C Version 3.0, Princeton preprin
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