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Chinese Physics

Integrability of the spin-1 XXX chain with boundary impurities and their Bethe ansatz

Bo-Yu Hou, Shi Kang-Jie, Rui‐Hong Yue, Shao-you Zhao A

Published Mar 1, 2000• 1 citation
Publisher

Abstract

By using the fusion method, we give the spin-1 XXX chain associated with sl 2 with two arbitrary spin boundary impurities. Then the exact diagonalized Hamiltonian of this model was obtained by the means of Bethe ansatz method.
DOI
10.1088/1009-1963/9/3/009

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Abstract The off-diagonal Bethe ansatz method is generalized to the integrable model associated with thesp(4) (orC2) 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 sameT−Qrelations obtained via conventional Bethe ansatz methods previously, while for the off-diagonal boundary condition case, the eigenvalues are given in terms of inhomogeneousT−Qrelations, which could not be obtained by the conventional Bethe ansatz methods. The method developed in this paper can be directly generalized to genericsp(2n) (i.e.,Cn) integrable model.