For most chiralities, semiconducting nanotubes display topologically protected end states of multiple degeneracies. We demonstrate using density matrix renormalization group based quantum chemistry tools that the presence of Coulomb interactions induces the formation of robust end spins. These are the close analogs of ferromagnetic edge states emerging in graphene nanoribbons. The interaction between the two ends is sensitive to the length of the nanotube, its dielectric constant, and the size of the end spins: for $S=1/2$ end spins, their interaction is antiferromagnetic, while for $S>1/2$, it changes from antiferromagnetic to ferromagnetic as the nanotube length increases. The interaction between end spins can be controlled by changing the dielectric constant of the environment, thereby providing a possible platform for two-spin quantum manipulations.

中文翻译：

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碳纳米管中拓扑保护的相关末端自旋形成。

对于大多数手性而言，半导体纳米管显示出多个简并性的受拓扑保护的最终状态。我们展示了使用基于密度矩阵重归一化组的量子化学工具，库仑相互作用的存在诱导了健壮的末端自旋的形成。这些是石墨烯纳米带中出现的铁磁边缘态的紧密类似物。两端之间的相互作用对纳米管的长度，介电常数和端旋的大小敏感：$\mathrm{小号}=\mathrm{1个}/2$ 末端自旋，它们的相互作用是反铁磁性的，而对于 $\mathrm{小号}>\mathrm{1个}/2$，随着纳米管长度的增加，它从反铁磁性变为铁磁性。可以通过改变环境的介电常数来控制末端自旋之间的相互作用，从而为双自旋量子操作提供可能的平台。