AI 中文总结
研究与强关联自旋-s Takhtajan-Babujian链边界耦合的自旋-1/2杂质，通过边界共形场论、Bethe Ansatz等方法揭示其边界量子相变与多塔结构，建立统一框架描述杂质屏蔽等物理过程。
AI 中文摘要
我们研究与强关联自旋-s Takhtajan-Babujian链边界耦合的自旋-1/2杂质，该可积模型的低能物理由受扰SU(2)_{2s} Wess-Zumino-Witten共形场论描述。边界共形场理论确定弱耦合 regime 的低能普适类，而精确Bethe Ansatz方法揭示一系列边界量子相变，其中杂质束缚态出现并将希尔伯特空间重组为基于不同边界构型构建的多个激发塔。该塔重组为超越常规Kondo regime 的丰富边界相图提供组织原则。弱反铁磁耦合实现过屏蔽2s通道Kondo普适类，而更强耦合产生局域边界模式和定性新的屏蔽机制。为描述所得热力学，我们开发广义热力学Bethe Ansatz框架，其捕获所有 regime 下的多塔结构。杂质熵在过屏蔽Kondo regime 中重现边界共形场理论预测，但在边界束缚态出现后呈现显著非单调温度依赖，与大规模有限温度矩阵乘积算子模拟定量一致。补充动力学计算揭示杂质谱函数中尖锐阈值特征，直接追踪潜在的塔结构。综上，边界共形场理论、精确Bethe Ansatz、广义热力学Bethe Ansatz及张量网络模拟，为关联自旋-s链中的杂质屏蔽、边界束缚态形成及激发塔重构提供统一描述。
英文摘要
We study a spin-$\frac12$ impurity coupled to the boundary of a strongly correlated spin-$s$ Takhtajan--Babujian chain, an integrable model whose low-energy physics is described by a perturbed $SU(2)_{2s}$ Wess--Zumino--Witten conformal field theory. While boundary conformal field theory determines the low-energy universality class of the weak-coupling regime, exact Bethe Ansatz methods reveal a sequence of boundary quantum phase transitions in which impurity-bound states emerge and reorganize the Hilbert space into multiple excitation towers built on distinct boundary configurations. This tower restructuring provides the organizing principle for a rich boundary phase diagram extending beyond the conventional Kondo regime. Weak antiferromagnetic coupling realizes the overscreened $2s$-channel Kondo universality class, whereas stronger couplings generate localized boundary modes and qualitatively new screening mechanisms. To describe the resulting thermodynamics, we develop a generalized thermodynamic Bethe Ansatz framework that captures the multi-tower structure across all regimes. The impurity entropy reproduces the boundary conformal field theory prediction in the overscreened Kondo regime but develops pronounced nonmonotonic temperature dependence once boundary-bound states appear, in quantitative agreement with large-scale finite-temperature matrix-product-operator simulations. Complementary dynamical calculations reveal sharp threshold features in the impurity spectral function that directly track the underlying tower structure. Together, boundary conformal field theory, exact Bethe Ansatz, generalized thermodynamic Bethe Ansatz, and tensor-network simulations provide a unified description of impurity screening, boundary-bound-state formation, and excitation-tower reconstruction in a correlated spin-$s$ chain.
Comments36 pages, 10 figures
