On Bethe eigenvectors and higher transfer matrices for supersymmetric spin chains

Abstract

We study the ${\mathfrak{gl}}_{m|n}$ XXX spin chains defined on tensor products of highest ${\mathfrak{gl}}_{m|n}$-modules. We show that the on-shell Bethe vectors are eigenvectors of higher transfer matrices and compute the corresponding eigenvalues, confirming Conjecture 5.15 of arXiv:2007.15573 and extending the main results of arXiv:0605015 to supersymmetric case. We then take the classical limits and obtain the corresponding results for the ${\mathfrak{gl}}_{m|n}$ Gaudin models.

37 pages. Extending the results of arXiv:0605015 and arXiv:0804.2822

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Cited by in corpus (1)

• A note on the quantum Berezinian for the double Yangian of the Lie superalgebra ${\mathfrak{gl}}_{m|n}$