Nonfreeness and related functionals for measuring correlation in many-fermion states

Abstract

This article is a brief review of "nonfreeness" and related measures of "correlation" for many-fermion systems. The many-fermion states we deem "uncorrelated" are the gauge-invariant quasi-free states. Uncorrelated states of systems of finitely many fermions we call simply "free" states. Slater determinant states are free; all other free states are "substates" of Slater determinant states or limits of such. The nonfreeness of a many-fermion state equals the minimum of its entropy relative to all free states. Correlation functionals closely related to nonfreeness can be defined in terms of R\'enyi entropies; nonfreeness is the one that uses Shannon entropy. These correlation functionals all share desirable additivity and monotonicity properties, but nonfreeness has some additional attractive properties.