$\mathbf{Z}_{n}$时钟模型和$so(n)_2$非阿贝尔任意子链：对称性、可积点和低能性质
$\mathbf{Z}_{n}$ clock models and chains of $so(n)_2$ non-Abelian anyons: symmetries, integrable points and low energy properties
摘要：
我们研究了两个族的量子模型，这些模型以前曾被用来研究一维关联物质中拓扑对称性的影响。在某些$\mathbf{Z}_n$量子钟模型、推广伊辛模型的自旋链和由奇数$n$的$so(n)_2$融合范畴构造的非阿贝尔任意子链之间，观察到了各种惊人的相似之处，两者都受到周期性边界条件的约束。尽管这两种类型的量子链之间存在差异，例如，它们的希尔伯特空间被局域自旋态的张量积或任意子的熔合路径所覆盖，晶格模型的对称性被证明是密切相关的。此外，在描述自旋和任意子之间相互作用的参数之间的适当映射下，各个哈密顿量共享它们的部分能谱（尽管它们的简并可能不同）。这种自旋-任意子的对应关系可以通过微调耦合常数得到精确可解的模型。我们表明，时钟模型和任意子链的可积性的代数结构是相同的。对于$n=3,5,7$，我们进行了广泛的有限尺寸的研究-数值和精确解的基础上-这些模型映射出他们的基态相图，并确定描述其低能量行为的有效场论。我们观察到，在可积点的连续极限可以描述的理性共形场论与扩展的对称代数，可以与离散的晶格模型。
英文摘要：
We study two families of quantum models which have been used previously to investigate the effect of topological symmetries in one-dimensional correlated matter. Various striking similarities are observed between certain $\mathbf{Z}_n$ quantum clock models, spin chains generalizing the Ising model, and chains of non-Abelian anyons constructed from the $so(n)_2$ fusion category for odd $n$, both subject to periodic boundary conditions. In spite of the differences between these two types of quantum chains, e.g.\ their Hilbert spaces being spanned by tensor products of local spin states or fusion paths of anyons, the symmetries of the lattice models are shown to be closely related. Furthermore, under a suitable mapping between the parameters describing the interaction between spins and anyons the respective Hamiltonians share part of their energy spectrum (although their degeneracies may differ). This spin-anyon correspondence can be extended by fine-tuning of the coupling constants leading to exactly solvable models. We show that the algebraic structures underlying the integrability of the clock models and the anyon chain are the same. For $n=3,5,7$ we perform an extensive finite size study -- both numerical and based on the exact solution -- of these models to map out their ground state phase diagram and to identify the effective field theories describing their low energy behaviour. We observe that the continuum limit at the integrable points can be described by rational conformal field theories with extended symmetry algebras which can be related to the discrete ones of the lattice models.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
