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arXiv:hep-th/0512273 · Journal of Statistical Mechanics Theory and Experiment

Structure of the two-boundaryXXZmodel with non-diagonal boundary terms

Alexander Nichols

Published Feb 27, 2006• 9 citations
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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.

DOI
10.1088/1742-5468/2006/02/l02004

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Abstract The Bose–Hubbard model is a paradigm for the study of strongly correlated bosonic systems. We study the two-site Bose–Hubbard model with generic integrable open boundaries specified by the most general non-diagonal reflecting matrices. Besides the inhomogeneous parameters, the model itself has three free boundary parameters, which break the U(1)-symmetry, in other words, break the particle number conservation. The Hamiltonian H under these circumstances is constructed. With the help of the off-diagonal Bethe Ansatz method, we successfully obtain the corresponding Bethe Ansatz equations as well as the eigenvalues.