A Q-operator for open spin chains II: boundary factorization

TL;DR

This paper extends the factorization formalism of Baxter's Q-operators to open spin chains by deriving a boundary factorization identity for solutions of the reflection equation in the quantum affine rak{sl}_2 case.

Contribution

It introduces a boundary factorization identity for solutions of the reflection equation, enabling the construction of Q-operators for open spin chains within a representation-theoretical framework.

Findings

Derived a boundary factorization identity for solutions of the reflection equation.

Extended the Q-operator formalism to open spin chains with boundary conditions.

Utilized universal K-matrices for quantum affine algebras in the derivation.

Abstract

One of the features of Baxter's Q-operators for many closed spin chain models is that all transfer matrices arise as products of two Q-operators with shifts in the spectral parameter. In the representation-theoretical approach to Q-operators, underlying this is a factorization formula for L-operators (solutions of the Yang-Baxter equation associated to particular infinite-dimensional representations). To have such a formalism to open spin chains, one needs a factorization identity for solutions of the reflection equation (boundary Yang-Baxter equation) associated to these representations. In the case of quantum affine $\mathfrak{sl}_2$ and diagonal K-matrices, we derive such an identity using the recently formulated theory of universal K-matrices for quantum affine algebras.