Spin entanglement in atoms and molecules

TL;DR

This paper introduces a local spin entanglement length derived from ab-initio methods, revealing enhanced spin entanglement in atomic shells and bonds, and reinterprets the electron localization function in terms of entanglement ratios.

Contribution

It proposes a new local entanglement measure based on Kohn-Sham orbitals and links it to the electron localization function, providing insights into spin entanglement in inhomogeneous systems.

Findings

Spin entanglement is enhanced in atomic shells.

Molecular bonds show increased spin entanglement.

The electron localization function relates to the ratio of local to homogeneous entanglement lengths.

Abstract

We investigate the effects of inhomogeneities on spin entanglement in many-electron systems from an ab-initio approach. The key quantity in our approach is the local spin entanglement length, which is derived from the local concurrence of the electronic system. Although the concurrence for an interacting systems is a highly nonlocal functional of the density, it does have a simple, albeit approximate expression in terms of Kohn-Sham orbitals. We show that the electron localization function -- well known in quantum chemistry as a descriptor of atomic shells and molecular bonds -- can be reinterpreted in terms of the ratio of the local entanglement length of the inhomogeneous system to the entanglement length of a homogenous system at the same density. We find that the spin entanglement is remarkably enhanced in atomic shells and molecular bonds.