New construction of eigenstates and separation of variables for SU(\(N\)) quantum spin chains
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Publication:1705984
DOI10.1007/JHEP09(2017)111zbMATH Open1382.81149arXiv1610.08032OpenAlexW3103091788WikidataQ62514346 ScholiaQ62514346MaRDI QIDQ1705984
Author name not available (Why is that?)
Publication date: 19 March 2018
Published in: (Search for Journal in Brave)
Abstract: We conjecture a new way to construct eigenstates of integrable XXX quantum spin chains with SU(N) symmetry. The states are built by repeatedly acting on the vacuum with a single operator Bgood(u) evaluated at the Bethe roots. Our proposal serves as a compact alternative to the usual nested algebraic Bethe ansatz. Furthermore, the roots of this operator give the separated variables of the model, explicitly generalizing Sklyanin's approach to the SU(N) case. We present many tests of the conjecture and prove it in several special cases. We focus on rational spin chains with fundamental representation at each site, but expect many of the results to be valid more generally.
Full work available at URL: https://arxiv.org/abs/1610.08032
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