Optimal scaling of persistent currents for interacting bosons on a ring

We consider the persistent currents induced by an artificial gauge field applied to interacting ultra-cold bosonic atoms in a tight ring trap. Using both analytical and numerical methods, we study the scaling of the persistent current amplitude with the size of the ring. In the strongly interacting regime we find a power-law scaling, in good agreement with the predictions of the Luttinger-liquid theory. By exploring all interaction regimes we find that the scaling is optimal, i.e. the current amplitude decreases slower with the system size, at intermediate interactions.