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This article is cited in 7 scientific papers (total in 7 papers)
Vertex Models and Spin Chains in Formulas and Pictures
Khazret S. Nirovabc, Alexander V. Razumovd a Institute for Nuclear Research of the Russian Academy of Sciences,
7a 60th October Ave., 117312 Moscow, Russia
b Mathematics and Natural Sciences, University of Wuppertal, 42097 Wuppertal, Germany
c Faculty of Mathematics, National Research University “Higher School of Economics”, 119048 Moscow, Russia
d NRC “Kurchatov Institute — IHEP”, 142281 Protvino, Moscow region, Russia
Abstract:
We systematise and develop a graphical approach to the investigations of quantum integrable vertex statistical models and the corresponding quantum spin chains. The graphical forms of the unitarity and various crossing relations are introduced. Their explicit analytical forms for the case of integrable systems associated with the quantum loop algebra ${\mathrm U}_q(\mathcal L(\mathfrak{sl}_{l + 1}))$ are given. The commutativity conditions for the transfer operators of lattices with a boundary are derived by the graphical method. Our consideration reveals useful advantages of the graphical approach for certain problems in the theory of quantum integrable systems.
Keywords:
quantum loop algebras, integrable vertex models, integrable spin models, graphical methods, open chains.
Received: March 19, 2019; in final form August 30, 2019; Published online September 13, 2019
Citation:
Khazret S. Nirov, Alexander V. Razumov, “Vertex Models and Spin Chains in Formulas and Pictures”, SIGMA, 15 (2019), 068, 67 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1504 https://www.mathnet.ru/eng/sigma/v15/p68
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