标题： $G_2$通过各向同性自旋-3链的可积点表征 显示英文标题

标题： $G_2$ Integrable Point Characterization via Isotropic Spin-3 Chains

摘要： 我们研究了在基本表示中具有局部自由度的$G_2$对称可积链的物理性质；鉴于可积性与临界点之间的典型联系，我们将模型的性质与共形不变的长距离行为假设进行了对比测试。 利用$G_2$特殊李代数与具有局部自旋-3 表示的$SU(2)$对称链之间的嵌入关系，我们通过精确对角化（ED）针对特定自旋子空间进行了数值分析，以及通过非阿贝尔密度矩阵重整化群（DMRG）进行了分析。 对动量分辨的 ED 谱的基本研究表明，低能系统可通过$(G_2)_1$Wess--Zumino--Witten（WZW）理论有效描述，但我们发现进一步数值表征共形数据存在挑战。 对该模型现象学的研究和控制可能对开发用于 Fibonacci 任意子的可访问模型具有重要意义。 显示英文摘要

摘要： We investigate the physical properties of $G_2$-symmetric integrable chains with local degrees of freedom in the fundamental representation; given the typical connection between integrability and critical points, we test the model's properties against a hypothesis of conformal-invariant long-distance behavior. Leveraging an embedding between the $G_2$ exceptional Lie algebra and $SU(2)$-symmetric chains with local spin-3 representations, we perform numerical analyses via exact diagonalization (ED) targeted at specific spin sectors, as well as via non-Abelian density-matrix renormalization group (DMRG). A basic study of the momentum-resolved ED spectrum suggests the low-energy system is effectively described by a $(G_2)_1$ Wess--Zumino--Witten (WZW) theory, but we find challenges in further numerical characterization of conformal data. The study and control of the phenomenology of this model may have implications for the development of accessible models for Fibonacci anyons.