Abstract
The exact solutions of the {D}_3^{(1)} model (or the so(6) quantum spin chain) with either periodic or general integrable open boundary conditions are obtained by using the off-diagonal 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}_n^{(1)} model directly.
Highlights
To study the spin chain associated with An Lie algebra with generic non-diagonal boundary reflections [26–28]
The exact solutions of the D3(1) model (or the so(6) quantum spin chain) with either periodic or general integrable open boundary conditions are obtained by using the off-diagonal Bethe Ansatz
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
Summary
Where the matrix elements are a = (u + 1)(u + 2), d = −u, b = u(u + 2), e = u(u + 1), f = 2, g = u + 2, and u is the spectral parameter. R1v2v(u) = V1 {R1v2v(−u − 2)}t2 V1 = V2 {R1v2v(−u − 2)}t1 V2, where P12 is the permutation operator with the matrix elements [P12]ikjl = δilδjk, ti denotes the transposition in the i-th space, and R21 = P12R12P12, and the crossing-matrix V is. The monodromy matrix satisfies the Yang-Baxter relation. The transfer matrix is given by the trace of monodromy matrix in the auxiliary space t(p)(u) = tr0T0v(u). From the Yang-Baxter relation (3.2), one can prove that the transfer matrices with different spectral parameters commute with each other, [t(p)(u), t(p)(v)] = 0.
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