Exact solution of the spin-s Heisenberg chain with generic non-diagonal boundaries

TL;DR

This paper extends the off-diagonal Bethe ansatz method to high spin su(2) integrable systems, deriving functional relations and demonstrating complete spectral solutions for the spin-s Heisenberg chain with non-diagonal boundaries.

Contribution

It introduces a generalized off-diagonal Bethe ansatz approach for high spin chains with non-diagonal boundaries, including new operator identities and T-Q relations.

Findings

Derived closed operator identities for T-Q relations.

Constructed inhomogeneous T-Q relations satisfying operator identities.

Numerical verification for the s=1 case confirms complete spectrum coverage.

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.