Local entanglement of electrons in 1D hydrogen molecule

TL;DR

This paper investigates how quantum entanglement entropy of electrons in a 1D hydrogen molecule varies with inter-nuclear distance, revealing different sensitivities of entropy and energy to electron interactions.

Contribution

It introduces a local entanglement entropy measure for the 1D hydrogen molecule and compares its behavior to total energy calculations, highlighting their differing sensitivities.

Findings

Entanglement entropy increases monotonically with inter-nuclear distance.

Local entropy peaks between nuclei and narrows as distance grows.

No entropy peculiarity at the stable molecule formation distance.

Abstract

The quantum entanglement entropy of the electrons in one-dimensional hydrogen molecule is quantified locally using an appropriate partitioning of the two-dimensional configuration space. Both the global and the local entanglement entropy exhibit a monotonic increase when increasing the inter-nuclear distance, while the local entropy remains peaked at the middle between the nuclei with its width decreasing. Our findings show that at the inter-nuclear distance where stable hydrogen molecule is formed, the quantum entropy shows no peculiarity thus indicating that the entropy and the energy measures display different sensitivity with respect to the interaction between the two identical electrons involved. One possible explanation is that the calculation of the quantum entropy does not account explicitly for the distance between the nuclei, which contrasts to the total energy calculation where the energy minimum depends decisively on that distance. The numerically exact and the time-dependent quantum Monte Carlo calculations show close results.