Rectangular Recurrence Relations in 𝖌𝔩ₙ and 𝔬₂ₙ₊₁ Invariant Integrable Models

Abstract

A new method is introduced to derive general recurrence relations for off-shell Bethe vectors in quantum integrable models with either type 𝖌𝔩ₙ or type 𝔬₂ₙ₊₁ symmetries. These recurrence relations describe how to add a single parameter 𝓏 to specific subsets of Bethe parameters, expressing the resulting Bethe vector as a linear combination of monodromy matrix entries that act on Bethe vectors which do not depend on 𝓏. We refer to these recurrence relations as rectangular because the monodromy matrix entries involved are drawn from the upper-right rectangular part of the matrix. This construction is achieved within the framework of the zero-mode method.