Fermionic entanglement and quantum correlation measures in molecules

TL;DR

This paper investigates fermionic entanglement and quantum correlations in the water molecule's electronic states using advanced measures, analyzing their behavior across different internuclear distances and in the dissociation limit.

Contribution

It introduces new entanglement measures and provides a detailed analysis of electronic correlations in molecules, extending understanding of quantum states in molecular systems.

Findings

Total up-down entanglement varies with internuclear distance.

New measures like up-down two-body mutual information reveal detailed correlation structures.

Dissociation limit analysis shows how correlations evolve in the ground and thermal states.

Abstract

We analyze fermionic entanglement and correlation measures in the ground and the low temperature thermal state of the water molecule as a function of the internuclear distance in the context of the full configuration interaction approach. The aim is to obtain a general entanglement based characterization of the electronic eigenstates. We consider first the spin-up - spin-down partition and the associated Schmidt decomposition, examining the total up-down entanglement of the electronic wave function. We then consider the one- and two-body entanglement derived from the one- and two-body reduced density matrices (DMs), which measure both the deviation of the state from a Slater Determinant (SD) as well as the up-down correlation at the two-body level. All blocks of these DMs are examined. We also introduce and analyze new measures like the up-down two-body mutual information and two types of two-body negativities, the latter measuring the "inner" entanglement of the reduced two-body DMs, i.e., their deviation from a convex mixture of SDs. Finally, the dissociation limit is also analyzed, considering both the exact ground state (GS) as well as the thermal state in the zero temperature limit, representing the projector onto the "GS band" of almost degenerate lowest lying eigenstates.