230 research outputs found
Bethe Ansatz solution for quantum spin-1 chains with boundary terms
The procedure for obtaining integrable open spin chain Hamiltonians via
reflection matrices is explicitly carried out for some three-state vertex
models. We have considered the 19-vertex models of Zamolodchikov-Fateev and
Izergin-Korepin, and the -graded 19-vertex models with and
invariances. In each case the eigenspectrum is determined by
application of the coordinate Bethe Ansatz.Comment: 24 pages, LaTex, some misprints remove
Reflection K-Matrices for 19-Vertex Models
We derive and classify all regular solutions of the boundary Yang-Baxter
equation for 19-vertex models known as Zamolodchikov-Fateev or
model, Izergin-Korepin or model, sl(2|1) model and osp(2|1)
model. We find that there is a general solution for and sl(2|1)
models. In both models it is a complete K-matrix with three free parameters.
For the and osp(2|1) models we find three general solutions,
being two complete reflection K-matrices solutions and one incomplete
reflection K-matrix solution with some null entries. In both models these
solutions have two free parameters. Integrable spin-1 Hamiltonians with general
boundary interactions are also presented. Several reduced solutions from these
general solutions are presented in the appendices.Comment: 35 pages, LaTe
Nonstandard coproducts and the Izergin-Korepin open spin chain
Corresponding to the Izergin-Korepin (A_2^(2)) R matrix, there are three
diagonal solutions (``K matrices'') of the boundary Yang-Baxter equation. Using
these R and K matrices, one can construct transfer matrices for open integrable
quantum spin chains. The transfer matrix corresponding to the identity matrix
K=1 is known to have U_q(o(3)) symmetry. We argue here that the transfer
matrices corresponding to the other two K matrices also have U_q(o(3))
symmetry, but with a nonstandard coproduct. We briefly explore some of the
consequences of this symmetry.Comment: 7 pages, LaTeX; v2 has one additional sentence on the degeneracy
patter
Integrable open-boundary conditions for the supersymmetric t-J model. The quantum group invariant case
We consider integrable open--boundary conditions for the supersymmetric t--J
model commuting with the number operator and . Four families, each
one depending on two arbitrary parameters, are found. We find the relation
between Sklyanin's method of constructing open boundary conditions and the one
for the quantum group invariant case based on Markov traces. The eigenvalue
problem is solved for the new cases by generalizing the Nested Algebraic Bethe
ansatz of the quantum group invariant case (which is obtained as a special
limit). For the quantum group invariant case the Bethe ansatz states are shown
to be highest weights of .Comment: Latex, 24 pages. Some new comments and references. Final version to
appear in Nucl. Phys.
D_{n+1}^(2) Reflection K-matrices
We investigate the possible regular solutions of the boundary Yang-Baxter
equation for the vertex models associated to the D_{n+1}^(2) affine Lie
algebra. We have classified them in terms of three types of K-matrices. The
first one have n+2 free parameters and all the matrix elements are non-null.
The second solution is given by a block diagonal matrix with just one free
parameter. It turns out that for n even there exists a third class of K-matrix
withou free parameter.Comment: 18 pages, Late
, and reflection K-matrices
We investigate the possible regular solutions of the boundary Yang-Baxter
equation for the vertex models associated with the ,
and affine Lie algebras. We find three types of solutions with
, and 1 free parameters,respectively. Special cases and all diagonal
solutions are presented separately.Comment: 22 pages, LaTe
Boundary K-matrices for the XYZ, XXZ AND XXX spin chains
The general solutions for the factorization equations of the reflection
matrices for the eight vertex and six vertex models (XYZ, XXZ
and XXX chains) are found. The associated integrable magnetic Hamiltonians are
explicitly derived, finding families dependig on several continuous as well as
discrete parameters.Comment: 13 page
Nonlocal, noncommutative picture in quantum mechanics and distinguished canonical maps
Classical nonlinear canonical (Poisson) maps have a distinguished role in
quantum mechanics. They act unitarily on the quantum phase space and generate
-independent quantum canonical maps. It is shown that such maps act in
the noncommutative phase space as dictated by the classical covariance. A
crucial observation made is that under the classical covariance the local
quantum mechanical picture can become nonlocal in the Hilbert space. This
nonlocal picture is made equivalent by the Weyl map to a noncommutative picture
in the phase space formulation of the theory. The connection between the
entanglement and nonlocality of the representation is explored and specific
examples of the generation of entanglement are provided by using such concepts
as the generalized Bell states. That the results have direct application in
generating vacuum soliton configurations in the recently popular scalar field
theories of noncommutative coordinates is also demonstrated.Comment: 14 pages, one figur
Analytical Bethe Ansatz for quantum-algebra-invariant open spin chains
We determine the eigenvalues of the transfer matrices for integrable open
quantum spin chains which are associated with the affine Lie algebras
, and which have the
quantum-algebra invariance U_q(C_n), U_q(B_n), U_q(C_n), U_q(D_n)$,
respectively.Comment: 14 pages, latex, no figures (a character causing latex problem is
removed
Exact solution of the invariant quantum spin chains
The Nested Bethe Ansatz is generalized to open boundary conditions. This is
used to find the exact eigenvectors and eigenvalues of the vertex
model with fixed open boundary conditions and the corresponding
invariant hamiltonian.
The Bethe Ansatz equations obtained are solved in the thermodynamic limit
giving the vertex model free energy and the hamiltonian ground state energy
including the corresponding boundary contributions.Comment: 29 page
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