Boundary non-local charges from the open spin chain

TL;DR

This paper derives boundary non-local charges for an open XXZ spin chain with specific boundary conditions, connecting them to field theory and revealing their symmetry properties and algebraic relations.

Contribution

It recovers boundary non-local charges from the spin chain perspective and demonstrates their commutation with the transfer matrix and algebraic structures.

Findings

Non-local charges commute with the transfer matrix under certain boundary conditions

Explicit demonstration of non-local charges commuting with blob algebra generators

Connection established between spin chain charges and sine Gordon model boundary charges

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.