Structure of the two-boundary XXZ model with non-diagonal boundary terms

Abstract

We study the integrable XXZ model with general non-diagonal boundary terms at both ends. The Hamiltonian is considered in terms of a two boundary extension of the Temperley-Lieb algebra. We use a basis that diagonalizes a conserved charge in the one-boundary case. The action of the second boundary generator on this space is computed. For the L-site chain and generic values of the parameters we have an irreducible space of dimension 2^L. However at certain critical points there exists a smaller irreducible subspace that is invariant under the action of all the bulk and boundary generators. These are precisely the points at which Bethe Ansatz equations have been formulated. We compute the dimension of the invariant subspace at each critical point and show that it agrees with the splitting of eigenvalues, found numerically, between the two Bethe Ansatz equations.

9 pages Latex. Minor corrections

References in corpus (3)

• Magic in the spectra of the XXZ quantum chain with boundaries at Delta=0 and Delta=-1/2
• One-boundary Temperley-Lieb algebras in the XXZ and loop models
• Bethe Ansatz derived from the functional relations of the open XXZ chain for new special cases

Cited by in corpus (7)

• The two-boundary Temperley-Lieb algebra
• Boundary operators in the O(n) and RSOS matrix models
• Critical dense polymers with Robin boundary conditions, half-integer Kac labels and ${\mathbb{Z}}_4$ fermions
• Boundary changing operators in the O(n) matrix model
• Generalized T-Q relations and the open spin-s XXZ chain with nondiagonal boundary terms
• Boundary energy of the general open XXZ chain at roots of unity
• Exotic Springer fibers for orbits corresponding to one-row bipartitions