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arXiv · 1705.09219

Norm of Bethe vectors in models with $\mathfrak{gl}(m|n)$ symmetry

A. Hutsalyuk·A. Liashyk·S. Z. Pakuliak·E. Ragoucy·N. A. Slavnov
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Abstract

We study quantum integrable models solvable by the nested algebraic Bethe ansatz and possessing $\mathfrak{gl}(m|n)$-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.

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A. Hutsalyuk, A. Liashyk, S. Z. Pakuliak, E. Ragoucy, N. A. Slavnov. 2020-01-31. Norm of Bethe vectors in models with $\mathfrak{gl}(m|n)$ symmetry. https://doi.org/10.1016/j.nuclphysb.2017.11.006

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