Entanglement of electron pairs extracted from a many-body system

TL;DR

This paper investigates the entanglement properties of electron pairs extracted from many-body systems, providing analytical formulas and examples for thermal entanglement in complex spin models.

Contribution

It introduces compact concurrence formulas for two-electron states with specific spin properties and analyzes their entanglement in realistic physical models.

Findings

Concurrence formulas are simplified for states with well-defined total spin projection.

Analytical expressions for thermal entanglement in anisotropic Heisenberg models are derived.

Electron pairs with antiparallel spins have entanglement characterized by scalar products with spin-flipped states.

Abstract

Entanglement of spins is analyzed for two electrons extracted from a mixed many electron state by projecting onto the two-electron subspace. The concurrence formulae are expressed in a compact form for states with a well defined square of the total spin projection. As an example, the thermal entanglement for a qubit pair with an anisotropic Heisenberg and the Dzyaloshinskii-Moriya interactions in an inhomogeneous magnetic field is given analytically. Remarkably, the concurrence of a pair of electrons with antiparallel spins and in a delocalised orbital state is given by the scalar product of the state with its spin-flipped state and not with the time-reversed state.