标题： 量子群不变$D^{(2)}_{n+1}$模型：Bethe假设和有限尺寸谱 显示英文标题

标题： Quantum-group-invariant $D^{(2)}_{n+1}$ models: Bethe ansatz and finite-size spectrum

摘要： 我们考虑与基于量子仿射代数$D^{(2)}_{n+1}$的 Jimbo R-矩阵相关的量子可积自旋链模型，其受两个离散变量$p=0,\dots, n$和$\varepsilon = 0, 1$参数化的量子群不变边界条件。我们发展了分析 Bethe 假设，用于之前未研究过的案例$\varepsilon = 1$以及任何$n$，并利用它来研究不同边界条件对基于秩-$2$代数$D^{(2)}_3$的量子自旋链的有限尺寸谱的影响。 之前在该模型上使用周期性边界条件的工作表明，当各向异性参数的范围为$0<\gamma<\pi/4$时，它是临界的，其标度极限由一个非紧致的共形场论描述，该理论具有与两个二维黑洞σ模型相关的连续自由度。 具有量子群不变边界条件的模型的标度极限取决于参数$\varepsilon$：类似于秩-$1$ $D^{(2)}_2$ 链的情况，我们发现晶格模型的对称性发生了自发破缺，共形权重的谱既有离散部分也有连续部分，对于$\varepsilon=1$。 对于$p=1$，后者与$D^{(2)}_2$链的谱相同，这应该对应于在边界存在的情况下与一个黑洞共形场论相关的非紧致膜。 对于$\varepsilon=0$，共形权重的谱是纯离散的。 显示英文摘要

摘要： We consider the quantum integrable spin chain models associated with the Jimbo R-matrix based on the quantum affine algebra $D^{(2)}_{n+1}$, subject to quantum-group-invariant boundary conditions parameterized by two discrete variables $p=0,\dots, n$ and $\varepsilon = 0, 1$. We develop the analytical Bethe ansatz for the previously unexplored case $\varepsilon = 1$ with any $n$, and use it to investigate the effects of different boundary conditions on the finite-size spectrum of the quantum spin chain based on the rank-$2$ algebra $D^{(2)}_3$. Previous work on this model with periodic boundary conditions has shown that it is critical for the range of anisotropy parameters $0<\gamma<\pi/4$, where its scaling limit is described by a non-compact CFT with continuous degrees of freedom related to two copies of the 2D black hole sigma model. The scaling limit of the model with quantum-group-invariant boundary conditions depends on the parameter $\varepsilon$: similarly as in the rank-$1$ $D^{(2)}_2$ chain, we find that the symmetry of the lattice model is spontaneously broken, and the spectrum of conformal weights has both discrete and continuous components, for $\varepsilon=1$. For $p=1$, the latter coincides with that of the $D^{(2)}_2$ chain, which should correspond to a non-compact brane related to one black hole CFT in the presence of boundaries. For $\varepsilon=0$, the spectrum of conformal weights is purely discrete.