Convexity of the entanglement entropy of Su(2n)-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 nonperturbative analytic relations for the Rényi entropies of those systems. These relations are valid for all subsystem sizes, particle numbers, and dimensions, and in arbitrary external trapping potentials