Convexity of the Entanglement Entropy of SU( 2 N )-Symmetric Fermions with Attractive Interactions

The positivity of the probability measure of attractively interacting systems of $2N$-component fermions enables the derivation of an exact convexity property for the ground-state energy of such systems. Using analogous arguments, applied to path-integral expressions for the entanglement entropy derived recently, we prove non-perturbative analytic relations for the R\'enyi entropies of those systems. These relations are valid for all sub-system sizes, particle numbers and dimensions, and in arbitrary external trapping potentials