Addendum to ``Integrability of Open Spin Chains with Quantum Algebra Symmetry''

TL;DR

This paper demonstrates the integrability of certain quantum-algebra-invariant open spin chains related to affine Lie algebras, expanding understanding of their mathematical properties without relying on crossing symmetry of the R-matrix.

Contribution

It proves the integrability of open spin chains associated with affine Lie algebras $A^{(1)}_n$ for $n>1$, without requiring crossing symmetry of the R-matrix.

Findings

Open spin chains with affine Lie algebra symmetry are integrable.

Integrability holds without crossing symmetry of the R-matrix.

Applicable to a broad class of quantum-algebra-invariant chains.

Abstract

We show that the quantum-algebra-invariant open spin chains associated with the affine Lie algebras $A^{(1)}_n$ for $n>1$ are integrable. The argument, which applies to a large class of other quantum-algebra-invariant chains, does not require that the corresponding $R$ matrix have crossing symmetry.