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An algebraic representation for correlation functions in integrable spin chains

Michio Jimbo

Springer eBooksMar 13, 20090 citations

Generalized algebraic framework for open spin chains

Ladislav Hlavatý

An extension of the Sklyanin algebraic framework for construction of a commuting set of operators is presented. The conditions under which the operators can be interpreted as integrals of motion of an open spin chain with boundary conditions and nearest-neighbour interaction are investigated. An example based on the asymmetric six-vertex solutions of the YBE equation is given.

Journal of Physics A Mathematical and GeneralAug 21, 19946 citations

Algebraic Representation of Correlation Functions in Integrable Spin Chains

Herman E. Boos, M. Jimbo, T. Miwa +2 more

arXiv:hep-th/0601132Annales Henri PoincaréNov 24, 200666 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

The Spectrum of the Finite Open XX Quantum Spin Chain with Transverse Magnetic Boundary Fields via Orthogonal Polynomials

J. F. van Diejen, Andrés Soledispa Tibán, Adrián Vidal

Annales Henri PoincaréApr 9, 20251 citation

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

Open Spin Chains and Quadratic Algebras

Abstract

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Open Spin Chains and Quadratic Algebras

Abstract

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