# Relating correlation measures: the importance of the energy gap

## TL;DR

This paper explores the relationship between quantum information theoretical and chemical concepts of electron correlation, emphasizing the role of the energy gap in connecting these perspectives through models like the Hubbard and stretched H2.

## Contribution

It demonstrates how the energy gap within symmetry-adapted subspaces links multipartite quantum correlations and correlation energy in electronic systems.

## Key findings

- The energy gap is crucial for relating different correlation measures.
- Models like the Hubbard and stretched H2 illustrate the connection.
- Correlation measures vary with the energy gap and system parameters.

## Abstract

The concept of correlation is central to all approaches that attempt the description of many-body effects in electronic systems. Multipartite correlation is a quantum information theoretical property that is attributed to quantum states independent of the underlying physics. In quantum chemistry, however, the correlation energy (the energy not seized by the Hartree-Fock ansatz) plays a more prominent role. We show that these two different viewpoints on electron correlation are closely related. The key ingredient turns out to be the energy gap within the symmetry-adapted subspace. We then use a few-site Hubbard model and the stretched H$_2$ to illustrate this connection and to show how the corresponding measures of correlation compare.