The off-diagonal Bethe ansatz method is generalized to the integrable model associated with the sp(4) (or C 2 ) Lie algebra. By using the fusion technique, we obtain the complete operator product identities among the fused transfer matrices. These relations, together with some asymptotic behaviors and values of the transfer matrices at certain points, enable us to determine the eigenvalues of the transfer matrices completely. For the periodic boundary condition case, we recover the same T − Q relations obtained via conventional Bethe ansatz methods previously, while for the off-diagonal boundary condition case, the eigenvalues are given in terms of inhomogeneous T − Q relations, which could not be obtained by the conventional Bethe ansatz methods. The method developed in this paper can be directly generalized to generic sp(2n) (i.e., C n ) integrable model.
The so(5) (i.e., B 2 ) quantum integrable spin chains with both periodic and nondiagonal boundaries are studied via the off-diagonal Bethe Ansatz method. By using the fusion technique, sufficient operator product identities (comparing to those in [1]) to determine the spectrum of the transfer matrices are derived. For the periodic case, we recover the results obtained in [1], while for the non-diagonal boundary case, a new inhomogeneous T − Q relation is constructed. The present method can be directly generalized to deal with the so(2n + 1) (i.e., B n ) quantum integrable spin chains with general boundaries.
The exact solutions of the D (1) 3 model (or the so(6) quantum spin chain) with either periodic or general integrable open boundary conditions are obtained by using the offdiagonal Bethe Ansatz. From the fusion, the complete operator product identities are obtained, which are sufficient to enable us to determine spectrum of the system. Eigenvalues of the fused transfer matrices are constructed by the T − Q relations for the periodic case and by the inhomogeneous T − Q one for the non-diagonal boundary reflection case. The present method can be generalized to deal with the D (1) n model directly.
New integrable B2 model with off-diagonal boundary reflections is proposed. The general solutions of the reflection matrix for the B2 model are obtained by using the fusion technique. We find that the reflection matrix has 7 free boundary parameters, which are used to describe the degree of freedom of boundary couplings, without breaking the integrability of the system. The new quantization conditions will induce the novel structure of the energy spectrum and the boundary states. The corresponding boundary effects can be studied based on the results in this paper. Meanwhile, the reflection matrix of high rank models associated with Bn algebra can also be obtained by using the method suggested in this paper.
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