When two identical fermions exchange their positions, their wave function gains a phase factor of $-1$. We show that this distance-independent effect can induce nonlocal entanglement in one-dimensional (1D) electron systems having Majorana fermions at the ends. It occurs in the system bulk and has a nontrivial temperature dependence. In a system having a single Majorana fermion at each end, the nonlocal entanglement has a Bell-state form at zero temperature and decays as the temperature increases, vanishing suddenly at a certain finite temperature. In a system having two Majorana fermions at each end, it is in a cluster-state form and its nonlocality is more noticeable at a finite temperature. By contrast, the thermal states of corresponding 1D spins do not have nonlocal entanglement.

中文翻译：

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Fermion交换统计量引起的一维热态的非局部纠缠

当两个相同的费米子交换位置时，​​它们的波函数获得的相位因子为 $-\mathrm{1个}$。我们表明，这种与距离无关的效应可以在端部具有马里亚纳费米子的一维（1D）电子系统中引起非局部纠缠。它发生在系统整体中，并且具有非平凡的温度依赖性。在每个末端只有一个马约拉那费米子的系统中，非局部纠缠在零温度下具有贝尔状态形式，并且随着温度的升高而衰减，在一定的有限温度下突然消失。在每个末端都有两个马约拉那费米子的系统中，它呈团簇状态，并且在一定温度下其非局部性更加明显。相反，相应的一维自旋的热态不具有非局部纠缠。