Defining relations on the Hamiltonians of $XXX$ and $XXZ$ $R$-matrices and new integrable spin-orbital chains
| dc.creator | Bibikov, P. N. | |
| dc.date | 2007-03-10 | |
| dc.date.accessioned | 2026-07-07T07:51:28Z | |
| dc.date.available | 2026-07-07T07:51:28Z | |
| dc.description | 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. | |
| dc.description | 9 pages | |
| dc.identifier | https://arxiv.org/abs/nlin/0703017 | |
| dc.identifier | http://arxiv.org/abs/nlin/0703017 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/125522 | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.title | Defining relations on the Hamiltonians of $XXX$ and $XXZ$ $R$-matrices and new integrable spin-orbital chains | |
| dc.type | text |