12 research outputs found
Completeness of the SO(4) Extended Bethe Ansatz for the One-Dimensional Hubbard Model
We show how to construct a complete set of eigenstates of the hamiltonian of
the one-dimensional Hubbard model on a lattice of even length . This is done
by using the nested Bethe Ansatz {\it and} the symmetry of the model.
We discuss in detail how the counting of independent eigenstates is carried
out.Comment: 33 pages, using latex, to appear in Nucl.Phys. B (FS
Exact solution of a t-J chain with impurity
We study the effects of an integrable impurity in a periodic t-J chain. The
impurity couples to both spin and charge degrees of freedom and has the
interesting feature that the interaction with the bulk can be varied
continuously without losing integrability. We first consider ground state
properties close to half-filling in the presence of a small bulk magnetic
field. We calculate the impurity contributions to the (zero temperature)
susceptibilities and the low temperature specific heat and determine the
high-temperature characteristics of the impurity. We then investigate transport
properties by computing the spin and charge stiffnesses at zero temperature.
Finally the impurity phase--shifts are calculated and the existence of an
impurity bound state in the holon sector is established.Comment: 33 pages Latex, figures include
On the Scaling Limit of the 1D Hubbard Model at Half Filling
The dispersion relations and S-matrix of the one-dimensional Hubbard model at
half filling are considered in a certain scaling limit. (In the process we
derive a useful small-coupling expansion of the exact lattice dispersion
relations.) The resulting scattering theory is consistently identified as that
of the SU(2) chiral-invariant Thirring (or Gross-Neveu) field theory,
containing both massive and massless sectors.Comment: 14 pages in harvmac, Tel-Aviv preprint TAUP 2203-9
Particles, Superparticles and Super Yang--Mills
This paper is concerned with theories describing spinning particles that are
formulated in terms of actions possessing either local world-line supersymmetry
or local fermionic {\it kappa} invariance. These classical actions are obtained
by adding a finite number of spinor or vector coordinates to the usual
space-time coordinates. Generalizing to superspace leads to corresponding types
of \lq spinning superparticle' theories in which the wave-functions are
superfields in some (generally reducible) representation of the Lorentz group.
A class of these spinning superparticle actions possesses the same spectrum as
ten-dimensional supersymmetric Yang--Mills theory, which it is shown can be
formulated in terms of either vector or spinor superfields satisfying
supercovariant constraints. The models under consideration include some that
were known previously and some new ones.Comment: 45 pages, QMW-93-0
Doped Heisenberg chains: spin-S generalizations of the supersymmetric t-J model
A family of exactly solvable models describing a spin-S Heisenberg chain
doped with mobile spin-(S-1/2) carriers is constructed from gl(2|1)-invariant
solutions of the Yang-Baxter equation. The models are generalizations of the
supersymmetric t-J model which is obtained for S=1/2. We solve the model by
means of the algebraic Bethe Ansatz and present results for the zero
temperature and thermodynamic properties. At low temperatures the models show
spin charge separation, i.e. contain contributions of a free bosonic theory in
the charge sector and an SU(2)-invariant theory describing the magnetic
excitations. For small carrier concentration the latter can be decomposed
further into an SU(2) level-2S Wess-Zumino-Novikov-Witten model and the minimal
unitary model M_p with p=2S+1.Comment: LaTeX, 24 pp. incl. 4 figure
Faceting Transition in an Exactly Solvable Terrace-Ledge-Kink model
We solve exactly a Terrace-Ledge-Kink (TLK) model describing a crystal
surface at a microscopic level. We show that there is a faceting transition
driven either by temperature or by the chemical potential that controls the
slope of the surface. In the rough phase we investigate thermal fluctuations of
the surface using Conformal Field Theory.Comment: 27 pages, 18 EPS figure
Exact thermodynamics and Luttinger liquid properties of the integrable t-J model
A Trotter-Suzuki mapping is used to calculate the finite-temperature
properties of the one-dimensional supersymmetric model. This approach
allows for the exact calculation of various thermodynamical properties by means
of the quantum transfer matrix (QTM). The free energy and other interesting
quantities are obtained such as the specific heat and compressibility. For the
largest eigenvalue of the QTM leading to the free energy a set of just two
non-linear integral equations is presented. These equations are studied
analytically and numerically for different particle densities and temperatures.
The structure of the specific heat is discussed in terms of the elementary
charge as well as spin excitations. Special emphasis is placed on the study of
the low-temperature behavior confirming scaling predictions by conformal field
theory and Luttinger liquid theory. To our knowledge this is the first complete
investigation of a strongly correlated electron system on a lattice at finite
temperature.Comment: 27 pages, Latex, 9 Post-Script figures, uses graphicx and amsmat
Scattering Matrix and Excitation Spectrum of the Hubbard Model
We consider the one-dimensional Hubbard model at half filling. We show that
both excitation spectrum and S-matrix are determined by the SO(4) symmetry of
the model. The complete set of excitations is given by the scattering states
four elementary excitations, which form the fundamental representation of
SO(4). We evaluate the exact S-matrix, which satisfies the Yang-Baxter
relation. The results for the repulsive and attractive Hubbard model are
related by an interchange of spin and charge degrees of freedom.Comment: 8 pages, jyTeX (macro included - just TeX the file) ITP-SB-93-4
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
Scaling Limit of the Ising Model in a Field
The dilute A_3 model is a solvable IRF (interaction round a face) model with
three local states and adjacency conditions encoded by the Dynkin diagram of
the Lie algebra A_3. It can be regarded as a solvable version of an Ising model
at the critical temperature in a magnetic field. One therefore expects the
scaling limit to be governed by Zamolodchikov's integrable perturbation of the
c=1/2 conformal field theory. Indeed, a recent thermodynamic Bethe Ansatz
approach succeeded to unveil the corresponding E_8 structure under certain
assumptions on the nature of the Bethe Ansatz solutions. In order to check
these conjectures, we perform a detailed numerical investigation of the
solutions of the Bethe Ansatz equations for the critical and off-critical
model. Scaling functions for the ground-state corrections and for the lowest
spectral gaps are obtained, which give very precise numerical results for the
lowest mass ratios in the massive scaling limit. While these agree perfectly
with the E_8 mass ratios, we observe one state which seems to violate the
assumptions underlying the thermodynamic Bethe Ansatz calculation. We also
analyze the critical spectrum of the dilute A_3 model, which exhibits massive
excitations on top of the massless states of the Ising conformal field theory.Comment: 29 pages, RevTeX, 11 PostScript figures included by epsf, using
amssymb.sty (v2.2