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

TL;DR

This paper demonstrates that the XXZ open spin chain with general boundary conditions has a q-deformed Onsager algebra symmetry, extending Onsager's approach from the Ising model to this quantum integrable system.

Contribution

It introduces a q-deformed analogue of Onsager's algebra as the fundamental symmetry ensuring integrability of the XXZ open spin chain.

Findings

Existence of a q-deformed Onsager algebra symmetry

Construction of commuting nonlocal operators

Expression of transfer matrix and Hamiltonian in terms of these operators

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.