Local Entanglement of Electrons in 1D Hydrogen Molecule

The quantum entanglement entropy of the electrons in a 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 in the middle between the nuclei with its width decreasing. Our findings show that at the inter-nuclear distance where a 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.

Automated summary

This study quantifies the quantum entanglement entropy of electrons in a one-dimensional hydrogen molecule using an appropriate partitioning of the two-dimensional configuration space. The results show that both global and local entanglement entropy increase monotonically with increasing inter-nuclear distance, while the local entropy remains peaked in the middle between the nuclei with decreasing width. The study suggests that the entropy and the energy measures have different sensitivity to the interaction between the electrons involved, possibly due to the quantum entropy calculation not explicitly accounting for the distance between nuclei.