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 aq-deformed analogue of the Onsager’s algebra as fundamental non-Abelian symmetry whichensures the integrability of the model. This symmetry implies the existence of a finite set ofindependent mutually commuting nonlocal operators which form an Abelian subalgebra.The transfer matrix and local conserved quantities, for instance the Hamiltonian, areexpressed in terms of these nonlocal operators. It follows that Onsager’s originalapproach of the planar Ising model can be extended to the XXZ open spin chain.