论文标题
对称性受保护的拓扑阶段，超出了组：Q形成的双线性 - 骨化自旋链
Symmetry protected topological phases beyond groups: The q-deformed bilinear-biquadratic spin chain
论文作者
论文摘要
我们研究了$ so_q（3）$量子组不变型旋转1双线性式旋转链的相图，用于$ q> 1 $的实际值。数值计算表明，该链具有至少三个明显区别的阶段：霍尔丹烷相的手性类似物，一个二聚相和铁磁相。相比之下，以$ q = 1 $存在已知存在的扩展关键区域的对应物仍然难以捉摸。我们的结果表明，Haldane阶段未能在纠缠频谱中表现出两倍的退化性，但是在适当的$ Q $ Q $ - 纠缠汉密尔顿汉密尔顿汉密尔顿的合适的$ q $ quneration中，可以将其解释为Zeeman领域。相图的结构通过极端各向异性极限$ q \ to \ infty $中的分析计算确认。我们的结果表明，对于$ q $的不同选择，应将$ u_q [su（2）] $的对称性解释为一个单个家庭，而不是定义SPT阶段时单独的对称性，自然而然地导致了QSPT阶段的概念。
We study the phase diagram of the $SO_q(3)$ quantum group invariant spin-1 bilinear-biquadratic spin chain for real values of $q>1$. Numerical computations suggest that the chain has at least three clearly distinguished phases: A chiral analogue of the Haldane phase, a dimerized phase and a ferromagnetic phase. In contrast, the counterpart of the extended critical region that is known to exist for $q=1$ remains elusive. Our results show that the Haldane phase fails to exhibit a two-fold degeneracy in the entanglement spectrum but that the degeneracy is restored upon a suitable $q$-deformation of the entanglement Hamiltonian which can be interpreted as a Zeeman field. The structure of the phase diagram is confirmed through analytical calculations in the extreme anisotropic limit $q\to\infty$. Our results suggest that symmetries of the form $U_q[su(2)]$ for distinct choices of $q$ should be interpreted as one single family instead of separate symmetries when defining SPT phases, leading naturally to the notion of a qSPT phase.
