Abstract
The off-diagonal Bethe ansatz method is generalized to the high spin integrable systems associated with the su(2) algebra by employing the spin-s isotropic Heisenberg chain model with generic integrable boundaries as an example. With the fusion techniques, certain closed operator identities for constructing the functional T-Q relations and the Bethe ansatz equations are derived. It is found that a variety of inhomogeneous T-Q relations obeying the operator product identities can be constructed. Numerical results for two-site s=1 case indicate that an arbitrary choice of the derived T-Q relations is enough to give the complete spectrum of the transfer matrix.
Highlights
Based on the fundamental properties of the R-matrix and the K-matrices for quantum integrable models, a systematic method for solving the eigenvalue problem of integrable models with generic boundary conditions, i.e., the off-diagonal Bethe ansatz (ODBA) method was proposed in [56,57,58,59] and several long-standing models [56,57,58,59,60,61] were solved
The off-diagonal Bethe ansatz method is generalized to the high spin integrable systems associated with the su(2) algebra by employing the spin-s isotropic Heisenberg chain model with generic integrable boundaries as an example
In appendix A, we prove that each solution of our functional equations can be parameterized in terms of a variety of inhomogeneous T − Q relations
Summary
Throughout, Vi denotes a (2li + 1)-dimensional linear space (C2li+1) which endows an irreducible representation of su(2) algebra with spin li. The R-matrix Ri(jli,lj)(u), denoted as the spin-(li, lj) R-matrix, is a linear operator acting in Vi ⊗ Vj. The R-matrix satisfies the following quantum Yang-Baxter equation (QYBE) [20, 21]. R1(212 ,s)(u) defined in auxiliary space and spin-s (i.e., (2s + 1)-dimensional) quantum space is given by [15,16,17,18,19]. Where P(l) is a projector acting on the tensor product of two spin-s spaces and projects the tensor space into the irreducible subspace of spin-l (i.e., (2l + 1)-dimensional subspace). The fused K− matrices (e.g the spin-j K− matrix) is given by. The fused K{−a(}j)(u) matrices satisfy the following reflection equation [25, 52]. Α+(u + η) p+ + u + η where p+ and α+ are some boundary parameters
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