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Zapiski Nauchnykh Seminarov POMI, 2006, Volume 335, Pages 50–58
(Mi znsl208)
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This article is cited in 1 scientific paper (total in 1 paper)
Defining relations on the Hamiltonians of $XXX$ and $XXZ$ $R$-matrices and new integrable spin-orbital chains
P. N. Bibikov Saint-Petersburg State University
Abstract:
Several complete systems of integrability conditions on a spin chain Hamiltonian density matrix are presented. The corresponding formulas for $R$-matrices are also given. The latter is expressed via the local Hamiltonian density in the form similar to spin one half $XXX$ and $XXZ$ models. The result is applied to the problem of integrability of $SU(2)\times SU(2)$- and $SU(2)\times U(1)$-invariant spin-orbital chains (the Kugel–Homskii–Inagaki model). The eight new integrable cases are found. One of them corresponds to the Temperley–Lieb algebra,
the others three to the algebra associated with the $XXX$, $XXZ$ and graded $XXZ$ models. The last two $R$-matrices are also presented.
Received: 10.07.2006
Citation:
P. N. Bibikov, “Defining relations on the Hamiltonians of $XXX$ and $XXZ$ $R$-matrices and new integrable spin-orbital chains”, Questions of quantum field theory and statistical physics. Part 19, Zap. Nauchn. Sem. POMI, 335, POMI, St. Petersburg, 2006, 50–58; J. Math. Sci. (N. Y.), 143:1 (2007), 2723–2728
Linking options:
https://www.mathnet.ru/eng/znsl208 https://www.mathnet.ru/eng/znsl/v335/p50
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Abstract page: | 340 | Full-text PDF : | 60 | References: | 31 |
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