Geodesic
Defining relations on the Hamiltonians of $XXX$ and $XXZ$ $R$-matrices and new integrable spin-orbital chains
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 19, Tome 335 (2006), pp. 50-58

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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. 
@article{ZNSL_2006_335_a2,
     author = {P. N. Bibikov},
     title = {Defining relations on the {Hamiltonians} of $XXX$ and $XXZ$ $R$-matrices and new integrable spin-orbital chains},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {50--58},
     publisher = {mathdoc},
     volume = {335},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2006_335_a2/}
}
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P. N. Bibikov. Defining relations on the Hamiltonians of $XXX$ and $XXZ$ $R$-matrices and new integrable spin-orbital chains. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 19, Tome 335 (2006), pp. 50-58. http://geodesic.mathdoc.fr/item/ZNSL_2006_335_a2/