TY - JOUR

T1 - A Q-Operator for Open Spin Chains II: Boundary Factorization

AU - Cooper, Alec

AU - Vlaar, Bart

AU - Weston, Robert

N1 - Publisher Copyright:
© The Author(s) 2024.

PY - 2024/5

Y1 - 2024/5

N2 - 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 extend 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 sl2 and diagonal K-matrices, we derive such an identity using the recently formulated theory of universal K-matrices for quantum affine algebras.

AB - 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 extend 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 sl2 and diagonal K-matrices, we derive such an identity using the recently formulated theory of universal K-matrices for quantum affine algebras.

UR - http://www.scopus.com/inward/record.url?scp=85191348797&partnerID=8YFLogxK

U2 - 10.1007/s00220-024-04973-0

DO - 10.1007/s00220-024-04973-0

M3 - Article

SN - 0010-3616

VL - 405

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 5

M1 - 405

ER -