The Haldane state is a typical quantum and topological state of matter, which exhibits an edge state corresponding to symmetry-protected topological order in a one-dimensional integer spin chain. Here we propose a concept to design the Haldane state with one-half spins by making use of a chain composed of one-half spin clusters. If the clusters contain two spins, the ground state of a chain corresponds to the Affleck-Kennedy-Lieb-Tasaki state. We thus extend this knowledge to general clusters consisting of not only even, but odd numbers of one-half spins. In the case of an odd number of spins in the clusters, we present a concrete procedure to construct a field-induced Haldane state, and demonstrate the Haldane state in a five-spin cluster chain. Our concept is useful to understand quantum magnetism in real materials such as Fedotovite, consisting of six-spin clusters aligned in one dimension. Furthermore, the edge state designed by our flexible scheme can be utilized for a processing unit of quantum computation with recent progress on intended synthesis of organic materials, quantum dots, and optical lattices.

中文翻译：

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自旋1/2簇链中基于簇的Haldane状态

霍尔丹状态是物质的典型量子态和拓扑态，其在一维整数自旋链中表现出与对称保护的拓扑顺序相对应的边缘态。在这里，我们提出一个概念，通过利用由一半自旋簇组成的链来设计具有一半自旋的霍尔丹状态。如果簇包含两个自旋，则链的基态对应于Affleck-Kennedy-Lieb-Tasaki状态。因此，我们将这一知识扩展到不仅由偶数个奇数个二分之一的自旋组成的一般簇。在簇中自旋数奇数的情况下，我们提出了一个具体的过程来构建场诱导的Haldane状态，并在五旋簇链中证明了Haldane状态。我们的概念对于理解诸如Fedotovite，由一维排列的六纺丝簇组成。此外，通过我们灵活的方案设计的边缘状态可用于量子计算的处理单元，并且随着有机材料，量子点和光学晶格的预期合成方面的最新进展。