34 research outputs found
Bethe Ansatz derived from the functional relations of the open XXZ chain for new special cases
The transfer matrix of the general integrable open XXZ quantum spin chain
obeys certain functional relations at roots of unity. By exploiting these
functional relations, we determine the Bethe Ansatz solution for the transfer
matrix eigenvalues for the special cases that all but one of the boundary
parameters are zero, and the bulk anisotropy parameter is \eta = i\pi/3, i\pi/5
,... In an Addendum, these results are extended to the cases that any two of
the boundary parameters {\alpha_-, \alpha_+,\beta_-, \beta_+} are arbitrary and
the remaining boundary parameters are either \eta or i \pi/2.Comment: 13 pages, LaTeX; amssymb, no figures; v2: published version +
Addendum; v3: correct Eq. (3.40
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
Complete Bethe Ansatz solution of the open spin-s XXZ chain with general integrable boundary terms
We consider the open spin-s XXZ quantum spin chain with N sites and general
integrable boundary terms for generic values of the bulk anisotropy parameter,
and for values of the boundary parameters which satisfy a certain constraint.
We derive two sets of Bethe Ansatz equations, and find numerical evidence that
together they give the complete set of eigenvalues of the transfer
matrix. For the case s=1, we explicitly determine the Hamiltonian, and find an
expression for its eigenvalues in terms of Bethe roots.Comment: 23 pages -- Latex2e; misprints in appendix correcte
Bethe Ansatz solution of the open XXZ chain with nondiagonal boundary terms
We propose a set of conventional Bethe Ansatz equations and a corresponding
expression for the eigenvalues of the transfer matrix for the open spin-1/2 XXZ
quantum spin chain with nondiagonal boundary terms, provided that the boundary
parameters obey a certain linear relation.Comment: 11 pages, LaTeX; amssymb, amsmath, no figures; v2: citation adde
Generalized T-Q relations and the open spin-s XXZ chain with nondiagonal boundary terms
We consider the open spin-s XXZ quantum spin chain with nondiagonal boundary
terms. By exploiting certain functional relations at roots of unity, we derive
a generalized form of T-Q relation involving more than one independent Q(u),
which we use to propose the Bethe-ansatz-type expressions for the eigenvalues
of the transfer matrix. At most two of the boundary parameters are set to be
arbitrary and the bulk anisotropy parameter has values \eta = i\pi/2,
i\pi/4,... We also provide numerical evidence for the completeness of the
Bethe-ansatz-type solutions derived, using s = 1 case as an example.Comment: 23 pages. arXiv admin note: substantial text overlap with
arXiv:0901.3558; v2: published versio
Analytical Bethe Ansatz for closed and open gl(n)-spin chains in any representation
We present an "algebraic treatment" of the analytical Bethe Ansatz. For this
purpose, we introduce abstract monodromy and transfer matrices which provide an
algebraic framework for the analytical Bethe Ansatz. It allows us to deal with
a generic gl(n)-spin chain possessing on each site an arbitrary
gl(n)-representation. For open spin chains, we use the classification of the
reflection matrices to treat all the diagonal boundary cases. As a result, we
obtain the Bethe equations in their full generality for closed and open spin
chains. The classifications of finite dimensional irreducible representations
for the Yangian (closed spin chains) and for the reflection algebras (open spin
chains) are directly linked to the calculation of the transfer matrix
eigenvalues. As examples, we recover the usual closed and open spin chains, we
treat the alternating spin chains and the closed spin chain with impurity
A note on the IR limit of the NLIEs of boundary supersymmetric sine-Gordon model
We consider the infrared (IR) limit of the nonlinear integral equations
(NLIEs) for the boundary supersymmetric sine-Gordon (BSSG) model, previously
obtained from the NLIEs for the inhomogeneous open spin-1 XXZ quantum spin
chain with general integrable boundary terms, for values of the boundary
parameters which satisfy a certain constraint. In particular, we compute the
boundary S matrix and determine the "lattice - IR" relation for the BSSG
parameters.Comment: 18 page
A new current algebra and the reflection equation
We establish an explicit algebra isomorphism between the quantum reflection
algebra for the R-matrix and a new type of current algebra.
These two algebras are shown to be two realizations of a special case of
tridiagonal algebras (q-Onsager).Comment: 14 pages; v2: More details in Section 4; Typos corrected; References
added; To appear in Lett. Math. Phy