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

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

2005-12-21

arxiv.org/abs/hep-th/0512273v2

J.Stat.Mech.0602:L02004,2006

Physics

High Energy Physics

High Energy Physics - Theory

9 pages Latex. Minor corrections

Scientific paper

10.1088/1742-5468/2006/02/L02004

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.

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