30 April 2012
On factorizing \(F\)-matrices in \(\mathcal{Y}(sl_n)\) and \(\mathcal{U}_q(\widehat{sl}_n)\) spin chains (paper)
S.G. Mc Ateer and M. Wheeler
Abstract: We consider quantum spin chains arising from \(N\)-fold tensor products of the fundamental evaluation representations of \(\mathcal{Y}(sl_n)\) and \(\mathcal{U}_q(\widehat{sl}_n)\). Using the partial \(F\)-matrix formalism from the seminal work of Maillet and Sanchez de Santos, we derive a completely factorized expression for the \(F\)-matrix of such models and prove its equivalence to the expression obtained by Albert, Boos, Flume and Ruhlig. A new relation between the \(F\)-matrices and the Bethe eigenvectors of these spin chains is given.
(Journal of Statistical Mechanics: theory and experiment, also available from arXiv:1112.0839 [math-ph].)