Tzeng Yu-Chin, Dai Li, Chung Ming-Chiang, Amico Luigi, Kwek Leong-Chuan
Department of Physics, National Chung Hsing University, Taichung 40227, Taiwan.
Center of Theoretical Sciences, National Taiwan University, Taipei 10617, Taiwan.
Sci Rep. 2016 May 24;6:26453. doi: 10.1038/srep26453.
We study the entanglement structure and the topological edge states of the ground state of the spin-1/2 XXZ model with bond alternation. We employ parity-density matrix renormalization group with periodic boundary conditions. The finite-size scaling of Rényi entropies S2 and S∞ are used to construct the phase diagram of the system. The phase diagram displays three possible phases: Haldane type (an example of symmetry protected topological ordered phases), Classical Dimer and Néel phases, the latter bounded by two continuous quantum phase transitions. The entanglement and non-locality in the ground state are studied and quantified by the entanglement convertibility. We found that, at small spatial scales, the ground state is not convertible within the topological Haldane dimer phase. The phenomenology we observe can be described in terms of correlations between edge states. We found that the entanglement spectrum also exhibits a distinctive response in the topological phase: the effective rank of the reduced density matrix displays a specifically large "susceptibility" in the topological phase. These findings support the idea that although the topological order in the ground state cannot be detected by local inspection, the ground state response at local scale can tell the topological phases apart from the non-topological phases.
我们研究了具有键交替的自旋-1/2 XXZ模型基态的纠缠结构和拓扑边缘态。我们采用具有周期性边界条件的奇偶密度矩阵重整化群方法。利用Rényi熵S2和S∞的有限尺寸标度来构建系统的相图。相图展示了三种可能的相：霍尔丹型（对称保护拓扑有序相的一个例子）、经典二聚体相和奈尔相，后一种相由两个连续的量子相变界定。通过纠缠可转换性研究并量化了基态中的纠缠和非局域性。我们发现，在小空间尺度下，拓扑霍尔丹二聚体相内的基态是不可转换的。我们观察到的现象学可以用边缘态之间的关联来描述。我们发现纠缠谱在拓扑相中也表现出独特的响应：约化密度矩阵的有效秩在拓扑相中显示出特别大的“敏感性”。这些发现支持了这样一种观点，即尽管基态中的拓扑序不能通过局部检测来探测，但局部尺度上的基态响应可以区分拓扑相和非拓扑相。
