Abstract
We study quantum integrable models solvable by the nested algebraic Bethe ansatz and possessing gl(m|n)-invariant R-matrix. We compute the norm of the Hamiltonian eigenstates. Using the notion of a generalized model we show that the square of the norm obeys a number of properties that uniquely fix it. We also show that a Jacobian of the system of Bethe equations obeys the same properties. In this way we prove a generalized Gaudin hypothesis for the norm of the Hamiltonian eigenstates.
Highlights
In the present paper we prove the Gaudin hypothesis for integrable models with gl(m|n) symmetry described by the super-Yangian Y gl(m|n)
We begin with a sum formula for the scalar product of generic Bethe vectors obtained in [20]. Using this formula we find a recursion for the scalar product and specify it to the case of the norm
We considered a generalized quantum integrable model with gl(m|n)-invariant R-matrix
Summary
Our approach is very closed to the one of the work [3] It is based on the nested algebraic Bethe ansatz [15,16,17] and the notion of a generalized model [3, 18, 19] (see [6]). We specify this recursion to the case of the norm in section 7 and show that it coincides with the recursion for the Gaudin determinant. In this way we prove the generalized Gaudin hypothesis for the models with gl(m|n)-invariant R-matrix. In appendix C we find residues in the poles of the highest coefficients
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