Scalar products and norm of Bethe vectors in ${\mathfrak{o}}_{2n+1}$ invariant integrable models

Abstract

We compute scalar products of off-shell Bethe vectors in models with $o_{2n+1}$ symmetry. The scalar products are expressed as a sum over partitions of the Bethe parameter sets, the building blocks being the so-called highest coefficients. We prove some recurrence relations and a residue theorem for these highest coefficients, and prove that they are consistent with the reduction to $g{l}_n$ invariant models. We also express the norm of on-shell Bethe vectors as a Gaudin determinant.

38 pages; introduction improved nd conclusion added; more explanations on the gl(n) reduction

References in corpus (9)

• Zero modes method and form factors in quantum integrable models
• Form factors of the monodromy matrix entries in gl(2|1)-invariant integrable models
• Scalar products in GL(3)-based models with trigonometric R-matrix. Determinant representation
• A computation of an universal weight function for the quantum affine algebra U_q(\hat{\mathfrak{gl}}_N)
• The Nested Off-shell Bethe ansatz and O(N) Matrix Difference Equations
• Recurrence relations for off-shell Bethe vectors in trigonometric integrable models
• Algebraic Bethe ansatz for ${\mathfrak{o}}_{2n+1}$-invariant integrable models
• Norm of a Bethe Vector and the Hessian of the Master Function
• Exact overlaps for all integrable two-site boundary states of $\mathfrak{gl}(N)$ symmetric spin chains

Cited by in corpus (1)

• Effective Bethe Ansatz for Spin-1 Non-integrable Models