论文标题
代数Bethe Ansatz，用于开放的XXZ旋转链，具有非对角线边界术语，通过$ u _ {\ Mathfrak {Q}}} \ Mathfrak {SL} _2 $对称性
Algebraic Bethe Ansatz for the Open XXZ Spin Chain with Non-Diagonal Boundary Terms via $U_{\mathfrak{q}}\mathfrak{sl}_2$ Symmetry
论文作者
论文摘要
我们通过传统的代数Bethe Ansatz方法得出了一般开放XXZ旋转链的BETHE方程，其在Nepomechie约束下具有非对角线边界项[J.物理。 A 37（2004），433-440，Arxiv：hep-th/0304092]。由于代数结构克服了$ \ mathsf {u}（1）$对称性和缺乏参考状态的技术困难，在新的$ _ {\ u _ {\ mathfrak {q}}} \ Mathfrak {sl sl sl} $ riend ristrantiention中实现了两型temperley-lieb hamiltonian的代数结构。边缘上的模块[J.高能量物理。 2022（2022），否。 11，016，64页，arxiv：2207.12772]。通过证明$ u _ {\ mathfrak {q}} \ Mathfrak {SL} _2 $与两型temboundary temberley-lieb代数之间的schur-weyl二元性，建立了两个汉密尔顿人的等效性。在此框架中，尼波姆基条件证明是在量子组融合规则方面具有简单的代数解释。
We derive by the traditional algebraic Bethe ansatz method the Bethe equations for the general open XXZ spin chain with non-diagonal boundary terms under the Nepomechie constraint [J. Phys. A 37 (2004), 433-440, arXiv:hep-th/0304092]. The technical difficulties due to the breaking of $\mathsf{U}(1)$ symmetry and the absence of a reference state are overcome by an algebraic construction where the two-boundary Temperley-Lieb Hamiltonian is realised in a new $U_{\mathfrak{q}}\mathfrak{sl}_2$-invariant spin chain involving infinite-dimensional Verma modules on the edges [J. High Energy Phys. 2022 (2022), no. 11, 016, 64 pages, arXiv:2207.12772]. The equivalence of the two Hamiltonians is established by proving Schur-Weyl duality between $U_{\mathfrak{q}}\mathfrak{sl}_2$ and the two-boundary Temperley-Lieb algebra. In this framework, the Nepomechie condition turns out to have a simple algebraic interpretation in terms of quantum group fusion rules.
