On Bethe eigenvectors and higher transfer matrices for supersymmetric spin chains

TL;DR

This paper proves that on-shell Bethe vectors are eigenvectors of higher transfer matrices in supersymmetric spin chains and extends known results to the $rak{gl}_{m|n}$ case, also exploring classical limits for Gaudin models.

Contribution

It confirms a conjecture about eigenvectors and eigenvalues for supersymmetric spin chains, extending previous results to the $rak{gl}_{m|n}$ case and classical limits.

Findings

Bethe vectors are eigenvectors of higher transfer matrices

Eigenvalues are explicitly computed for supersymmetric models

Classical limits yield results for $rak{gl}_{m|n}$ Gaudin models

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.