Identification of an ideal correlation measure

Identify a correlation measure of the one-particle reduced density matrix that provides an appropriate and generally reliable coarse-graining variable for the cumulant correlation energy across the systems and deformations considered.

Background

The framework requires selecting a scalar correlation measure, such as the nonfreeness, the square-root measure, or the non-idempotency measure, to replace the full 1RDM dependence of the correlation functional. Different measures can produce substantially different approximations and correlation temperatures.

For the Hubbard dimer, symmetry and analytic solvability identify measures that reproduce exact or tight functional bounds. For more general molecular systems, however, the paper states that the appropriate measure cannot be selected in advance. The subsequent examples show that the particle-hole symmetrized entropy can describe some deformations but fails to capture others, motivating the unresolved task of determining which measure, or combination of measures, best represents correlation in broader settings.