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When two identical fermions exchange their positions, their wave functiongains phase factor $-1$. We show that this distance-independent effect caninduce nonlocal entanglement in one-dimensional (1D) electron systems havingMajorana fermions at the ends. It occurs in the system bulk and has nontrivialtemperature dependence. In a system having a single Majorana at each end, thenonlocal entanglement has a Bell-state form at zero temperature and decays astemperature increases, vanishing suddenly at certain finite temperature. In asystem having two Majoranas at each end, it is in a cluster-state form and itsnonlocality is more noticeable at finite temperature. By contrast, thermalstates of corresponding 1D spins do not have nonlocal entanglement.

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