{"title":"A Q-Operator for Open Spin Chains II: Boundary Factorization","authors":"Alec Cooper, Bart Vlaar, Robert Weston","doi":"10.1007/s00220-024-04973-0","DOIUrl":null,"url":null,"abstract":"<p>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 <span>\\(\\mathfrak {sl}_2\\)</span> and diagonal K-matrices, we derive such an identity using the recently formulated theory of universal K-matrices for quantum affine algebras.</p>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1007/s00220-024-04973-0","RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
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 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 \(\mathfrak {sl}_2\) and diagonal K-matrices, we derive such an identity using the recently formulated theory of universal K-matrices for quantum affine algebras.
许多封闭自旋链模型的巴克斯特 Q 运算符的特点之一是,所有转移矩阵都是两个 Q 运算符的乘积,谱参数有偏移。在 Q 运算符的表示理论方法中,其基础是 L 运算符(与特定无穷维表示相关的杨-巴克斯特方程的解)的因式分解公式。要把这种形式主义推广到开放自旋链,我们需要一个与这些表示相关的反射方程(边界杨-巴克斯特方程)解的因式分解标识。在量子仿射(\mathfrak {sl}_2\)和对角 K 矩的情况下,我们利用最近制定的量子仿射代数的通用 K 矩理论推导出了这样一个标识。
期刊介绍:
The mission of Communications in Mathematical Physics is to offer a high forum for works which are motivated by the vision and the challenges of modern physics and which at the same time meet the highest mathematical standards.