Boundary non-local charges from the open spin chain

Abstract

The $N$ site open XXZ quantum spin chain with a right non-diagonal boundary and special diagonal left boundary is considered. The boundary non-local charges originally obtained from a field theoretical viewpoint, for the sine Gordon model on the half line, are recovered from the spin chain point of view. Furthermore, the symmetry of the open spin chain is exhibited. More specifically, we show that certain non--local charges commute with the transfer matrix of the open spin chain, depending on the choice of boundary conditions. In addition, we show explicitly that for a special choice of the left boundary, one of the non--local charges, in a particular representation, commutes with each one of the generators of the blob algebra, and hence with the corresponding local Hamiltonian.