Nonlocal Entanglement of 1D Thermal States Induced by Fermion Exchange Statistics

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.