Nested algebraic Bethe ansatz for open spin chains with even twisted Yangian symmetry

Abstract

We present a nested algebraic Bethe ansatz for a one dimensional open spin chain whose boundary quantum spaces are irreducible ${\mathfrak{so}}_{2n}$- or ${\mathfrak{sp}}_{2n}$-representations and the monodromy matrix satisfies the defining relations of the Olshanskii twisted Yangian $Y^{\pm }({\mathfrak{gl}}_{2n})$. We use a generalization of the Bethe ansatz introduced by De Vega and Karowski which allows us to relate the spectral problem of a ${\mathfrak{so}}_{2n}$- or ${\mathfrak{sp}}_{2n}$-symmetric open spin chain to that of a ${\mathfrak{gl}}_n$-symmetric periodic spin chain. We explicitly derive the structure of the Bethe vectors and the nested Bethe equations.

36 pages; v.2: minor corrections, a trace formula for the Bethe vectors added

References in corpus (3)

• Functional relations from the Yang-Baxter algebra: Eigenvalues of the XXZ model with non-diagonal twisted and open boundary conditions
• Scalar products of Bethe vectors in the models with $\mathfrak{gl}(m|n)$ symmetry
• Discrete CMC surfaces in R^3 and discrete minimal surfaces in S^3. A discrete Lawson correspondence

Cited by in corpus (4)

• Nonstandard Bethe Ansatz equations for open O(N) spin chains
• Nested algebraic Bethe ansatz for orthogonal and symplectic open spin chains
• More on Affine Dynkin Quiver Yangians
• Gelfand-Tsetlin degeneration of shift of argument subalgebras in type D