Defining relations on the Hamiltonians of XXX and XXZ R-matrices and new integrable spin-orbital chains
Copyright policy )Defining relations on the Hamiltonians of XXX and XXZ R-matrices and new integrable spin-orbital chains
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.
9 pages
- St Petersburg University Russian Federation
Nonlinear Sciences - Exactly Solvable and Integrable Systems, \(XXZ\) model, FOS: Physical sciences, Groups and algebras in quantum theory and relations with integrable systems, \(XXX\) model, Exactly Solvable and Integrable Systems (nlin.SI), spin, Exactly solvable models; Bethe ansatz, Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics, \(R\)-matrix, Hamiltonian
Nonlinear Sciences - Exactly Solvable and Integrable Systems, \(XXZ\) model, FOS: Physical sciences, Groups and algebras in quantum theory and relations with integrable systems, \(XXX\) model, Exactly Solvable and Integrable Systems (nlin.SI), spin, Exactly solvable models; Bethe ansatz, Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics, \(R\)-matrix, Hamiltonian
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