Abstract
The double row transfer matrix of the open O(N) spin chain is diagonalized and the Bethe Ansatz equations are also derived by the algebraic Bethe Ansatz method including the so far missing case when the residual symmetry is O(2M+1)×O(2N−2M−1). In this case the boundary breaks the “rank” of the O(2N) symmetry leading to nonstandard Bethe Ansatz equations in which the number of Bethe roots is less than as it was in the periodic case. Therefore these cases are similar to soliton-nonpreserving reflections.
Highlights
A number of methods have been developed in the past for the calculation of the spectrum of quantum-integrable systems including coordinate, algebraic and analytic Bethe-Ansatz
The double row transfer matrix of the open O(N ) spin chain is diagonalized and the Bethe Ansatz equations are derived by the algebraic Bethe Ansatz method including the so far missing case when the residual symmetry is O(2M + 1) × O(2N − 2M − 1)
In this case the boundary breaks the ”rank” of the O(2N ) symmetry leading to nonstandard Bethe Ansatz equations in which the number of Bethe roots is less than as it was in the periodic case
Summary
A number of methods have been developed in the past for the calculation of the spectrum of quantum-integrable systems including coordinate, algebraic and analytic Bethe-Ansatz. In the third section the algebraic Bethe-Ansatz is described for open O(2N ) spin chains, which is the generalization of the periodic case [11]. Using this we construct Bethe-Ansatz equations for all O(2N ) K-matrices including the H = O(2M + 1) × O(2N − 2M − 1) case which was not studied previously. This Bethe-Ansatz method can be applied to the O(2N + 1) type spin chains and the results are summarized in the first appendix. We will see that the O(6) reflections can be obtained by fusion in the SU(4) model
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