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

Abstract

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.

Numerical renormalization group method for entanglement negativity at finite temperature

“…This provides the underlying mechanism of the linear dependence of T SD vs. J. Note that the entanglement sudden death also appears in other many-body systems at finite temperature [31][32][33].…”

“…N (ρ) is computable as long as Tr |ρ T A | is. Due to this computational advantage, the negativity has been widely used to study entanglement in many-body systems at finite temperature [25][26][27][28][29][30][31][32][33]. The numerical computation of the negativity N (ρ), however, becomes difficult, as the size of ρ becomes larger.…”

“…N (ρ) is computable as long as Tr |ρ T A | is. Due to this computational advantage, the negativity has been widely used to study entanglement in many-body systems at finite temperature [25][26][27][28][29][30][31][32][33].…”

Entanglement Negativity Spectrum of Random Mixed States: A Diagrammatic Approach

“…Expert readers may skip this part. Historically, LN has been shown to be useful in studying various quantum many-body systems including harmonic oscillator chains [34][35][36][37][38][39][40][41][42], quantum spin models [43][44][45][46][47][48][49][50][51][52], (1+1)d conformal and integrable field theories [18,[53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][68][69], topologically phases of matter [70][71][72][73][74][75][76], and in outof-equilibrium dynamics [77][78][79][80][81]…”

Entanglement negativity of fermions: Monotonicity, separability criterion, and classification of few-mode states

“…The entanglement negativity of topologically ordered phases in (2+1) dimensions were also studied [35][36][37][38]. The applicability of the negativity in characterizing finite-temperature systems [39][40][41][42] and out-of-equilibrium scenarios [40,[43][44][45] was also investigated. In addition to these literatures, there are other useful numerical frameworks to evaluate the entanglement negativity such as tree tensor network [46], Monte Carlo implementation of partial transpose [47,48], and rational interpolations [49].…”