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Zapiski Nauchnykh Seminarov POMI, 2006, Volume 335, Pages 50–58 (Mi znsl208)  

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
Full-text PDF (178 kB) Citations (1)
References:
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
English version:
Journal of Mathematical Sciences (New York), 2007, Volume 143, Issue 1, Pages 2723–2728
DOI: https://doi.org/10.1007/s10958-007-0159-5
Bibliographic databases:
UDC: 517.9
Language: Russian
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
Citation in format AMSBIB
\Bibitem{Bib06}
\by P.~N.~Bibikov
\paper Defining relations on the Hamiltonians of $XXX$ and $XXZ$ $R$-matrices and new integrable spin-orbital chains
\inbook Questions of quantum field theory and statistical physics. Part~19
\serial Zap. Nauchn. Sem. POMI
\yr 2006
\vol 335
\pages 50--58
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl208}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2269750}
\zmath{https://zbmath.org/?q=an:1122.82011}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2007
\vol 143
\issue 1
\pages 2723--2728
\crossref{https://doi.org/10.1007/s10958-007-0159-5}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34247395312}
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  • https://www.mathnet.ru/eng/znsl/v335/p50
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Abstract page:340
    Full-text PDF :60
    References:31
     
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