Boundary non-local charges from the open spin chain

Abstract

The N siteopen XXZ quantum spin chain with a right non-diagonal boundary and special diagonal left boundaryis considered. The boundary non-local charges originally obtained from a field theoreticalviewpoint, for the sine–Gordon model on the half line, are recovered from the spin chainpoint of view. Furthermore, the symmetry of the open spin chain is exhibited. Morespecifically, we show that certain non-local charges commute with the transfermatrix of the open spin chain, depending on the choice of boundary conditions. Inaddition, we show explicitly that for a special choice of the left boundary one of thenon-local charges, in a particular representation, commutes with each one of thegenerators of the blob algebra, and hence with the corresponding local Hamiltonian.