Abstract We investigate the effect of introducing a boundary inhomogeneity in the transfer matrix of an integrable open quantum spin chain. We find that it is possible to construct a local Hamiltonian, and to have quantum group symmetry. The boundary inhomogeneity has a profound effect on the Bethe ansatz solution.
Abstract We argue that the Hamiltonians for A 2 n ( 2 ) open quantum spin chains corresponding to two choices of integrable boundary conditions have the symmetries U q ( B n ) and U q ( C n ) , respectively. We find a formula for the Dynkin labels of the Bethe states (which determine the degeneracies of the corresponding eigenvalues) in terms of the numbers of Bethe roots of each type. With the help of this formula, we verify numerically (for a generic value of the anisotropy parameter) that the degeneracies and multiplicities of the spectra implied by the quantum group symmetries are completely described by the Bethe ansatz.
We review recent results on the Bethe Ansatz solutions for the eigenvalues of the transfer matrix of an integrable open XXZ quantum spin chain using functional relations which the transfer matrix obeys at roots of unity. First, we consider a case where at most two of the boundary parameters {{alpha−,alpha+,beta−,beta+}} are nonzero. A generalization of the Baxter T−Q equation that involves more than one independent Q is described. We use this solution to compute the boundary energy of the chain in the thermodynamic limit. We conclude the paper with a review of some results for the general integrable boundary terms, where all six boundary parameters are arbitrary.
Abstract Two branches of integrable open quantum-group invariant quantum spin chains are known. For one branch ( ), a complete Bethe ansatz solution has been proposed. However, the other branch ( ) has so far resisted solution. In an effort to address this problem, we consider here the simplest case n = 1. We propose a Bethe ansatz solution, which however is not complete, as it describes only the transfer-matrix eigenvalues with odd degeneracy. We also consider a proposal for the missing eigenvalues.