We examine the Onsager algebra symmetry of $τ^{(j)}$ -matrices in the superintegrable chiral Potts model. The comparison of Onsager algebra symmetry of the chiral Potts model with the $sl_2$ -loop algebra symmetry of six-vertex model at roots of unity is made from the aspect of functional relations using the $Q$ -operator and fusion matrices. The discussion of Bethe ansatz for both models is conducted in a uniform manner through the evaluation parameters of their symmetry algebras.We examine the Onsager algebra symmetry of $τ^{(j)}$-matrices in the superintegrable chiral Potts model. The comparison of Onsager algebra symmetry of the chiral Potts model with the $sl_2$-loop algebra symmetry of six-vertex model at roots of unity is made from the aspect of functional relations using the $Q$-operator and fusion matrices. The discussion of Bethe ansatz for both models is conducted in a uniform manner through the evaluation parameters of their symmetry algebras.

arXiv:cond-mat/0511543Dec 1, 20068 citations

Operator realizations of the q-deformed Heisenberg algebra

Hui-yun Pan, Zu Sen Zhao

Physics Letters AApr 1, 20014 citations

Q-deformed algebras and many-body physics

D. Galetti, Jose Tadeu Lunardi, B. M. Pimentel +1 more

Jan 1, 19950 citations

A deformed analogue of Onsager's symmetry in the XXZ open spin chain

Pascal Baseilhac, Kozo Koizumi

The XXZ open spin chain with general integrable boundary conditions is shown to possess a q-deformed analogue of the Onsager's algebra as fundamental non-abelian symmetry which ensures the integrability of the model. This symmetry implies the existence of a finite set of independent mutually commuting nonlocal operators which form an abelian subalgebra. The transfer matrix and local conserved quantities, for instance the Hamiltonian, are expressed in terms of these nonlocal operators. It follows that Onsager's original approach of the planar Ising model can be extended to the XXZ open spin chain.The XXZ open spin chain with general integrable boundary conditions is shown to possess a q-deformed analogue of the Onsager's algebra as fundamental non-abelian symmetry which ensures the integrability of the model. This symmetry implies the existence of a finite set of independent mutually commuting nonlocal operators which form an abelian subalgebra. The transfer matrix and local conserved quantities, for instance the Hamiltonian, are expressed in terms of these nonlocal operators. It follows that Onsager's original approach of the planar Ising model can be extended to the XXZ open spin chain.

Jan 1, 200555 citations

A deformed analogue of Onsager’s symmetry in the XXZ open spin chain

Pascal Baseilhac, Kozo Koizumi

The XXZ open spin chain with general integrable boundary conditions is shown to possess a q -deformed analogue of the Onsager's algebra as fundamental non-Abelian symmetry which ensures the integrability of the model. This symmetry implies the existence of a finite set of independent mutually commuting nonlocal operators which form an Abelian subalgebra. The transfer matrix and local conserved quantities, for instance the Hamiltonian, are expressed in terms of these nonlocal operators. It follows that Onsager's original approach of the planar Ising model can be extended to the XXZ open spin chain.The XXZ open spin chain with general integrable boundary conditions is shown to possess a q -deformed analogue of the Onsager's algebra as fundamental non-Abelian symmetry which ensures the integrability of the model. This symmetry implies the existence of a finite set of independent mutually commuting nonlocal operators which form an Abelian subalgebra. The transfer matrix and local conserved quantities, for instance the Hamiltonian, are expressed in terms of these nonlocal operators. It follows that Onsager's original approach of the planar Ising model can be extended to the XXZ open spin chain.

arXiv:hep-th/0507053Journal of Statistical Mechanics Theory and ExperimentOct 7, 200576 citations

A q-deformed harmonic oscillator from partial algebraization

A. Freitas, S. Salamó

NCimBJan 1, 20010 citations

We examine the Onsager algebra symmetry of

τ^{(j)}

-matrices in the superintegrable chiral Potts model. The comparison of Onsager algebra symmetry of the chiral Potts model with the

sl_2

-loop algebra symmetry of six-vertex model at roots of unity is made from the aspect of functional relations using the

Q

-operator and fusion matrices. The discussion of Bethe ansatz for both models is conducted in a uniform manner through the evaluation parameters of their symmetry algebras.