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

TL;DR

This paper demonstrates that fermion exchange statistics can induce nonlocal entanglement in 1D electron systems with Majorana fermions, showing temperature-dependent behavior and contrasting with spin systems.

Contribution

It reveals a novel mechanism for nonlocal entanglement driven by fermion exchange statistics in 1D systems with Majoranas, including detailed temperature effects.

Findings

Nonlocal entanglement can be induced by fermion exchange in 1D electron systems.

Entanglement exhibits temperature-dependent decay and sudden vanishing.

Spin system states do not show similar nonlocal entanglement.

Abstract

When two identical fermions exchange their positions, their wave function gains phase factor $-1$. 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 nontrivial temperature dependence. In a system having a single Majorana at each end, the nonlocal entanglement has a Bell-state form at zero temperature and decays as temperature increases, vanishing suddenly at certain finite temperature. In a system having two Majoranas at each end, it is in a cluster-state form and its nonlocality is more noticeable at finite temperature. By contrast, thermal states of corresponding 1D spins do not have nonlocal entanglement.