Local classical correlations between physical electrons in Hubbard systems

TL;DR

This paper shows that local electron correlations in Hubbard models are purely classical and can be measured via mutual information, linking local classical correlations to nonlocal entanglement.

Contribution

It proves that local correlations in Hubbard models conserving electron number are fully classical and relates local classical correlations to nonlocal entanglement.

Findings

Local nonfreeness equals mutual information between local natural orbitals.

Local electron correlations are fully classical in certain Hubbard models.

Nonlocal processes significantly influence local classical correlations.

Abstract

We demonstrate that the local nonfreeness, an unbiased measure of correlation between electrons at a single lattice site, can be computed as the mutual information between local natural spin orbitals. This leads us to prove a general result: local electron correlations in Hubbard-type models that conserve the orbital- and spin-resolved electron number are fully classical, since the local reduced density matrix is separable in the natural basis and no quantum correlations beyond entanglement are present. Finally, we compare different theoretical descriptions of magnetic and nonmagnetic states, showing that local classical correlations are drastically influenced by nonlocal processes. These results confirm the relation between local classical correlations within an open system and nonlocal entanglement and they provide a clear path for the study of the relationship between traditional quantum resources and the nonfreeness in terms of experimentally accessible quantities.