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

Abstract

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.

12 pages; LaTeX file with amssymb; v2: typos corrected, clarifications in the text; v3: minor changes in references, version to appear in JSTAT

References in corpus (2)

• An integrable structure related with tridiagonal algebras
• A new (in)finite dimensional algebra for quantum integrable models

Cited by in corpus (36)

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• Open spin chains with generic integrable boundaries: Baxter equation and Bethe ansatz completeness from SOV
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• The $q$-Onsager Algebra and the Universal Askey-Wilson Algebra
• Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra II
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• Counting solutions of the Bethe equations of the quantum group invariant open XXZ chain at roots of unity
• Closed hierarchy of Heisenberg equations in integrable models with Onsager algebra
• Conjectures on Hidden Onsager Algebra Symmetries in Interacting Quantum Lattice Models
• Generalised Onsager Algebra in Quantum Lattice Models
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• A compact presentation for the alternating central extension of the positive part of $U_q({\widehat{\mathfrak{sl}}}_2)$
• The $q-$Onsager algebra and multivariable $q-$special functions
• Higher rank classical analogs of the Askey-Wilson algebra from the $s{l}_N$ Onsager algebra
• Analogues of Lusztig's higher order relations for the q-Onsager algebra
• Generalized T-Q relations and the open spin-s XXZ chain with nondiagonal boundary terms
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• Bethe States of the integrable spin-s chain with generic open boundaries
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