Fractional periodicity of persistent current in coupled quantum rings

We study the transmission properties of a few-site Hubbard rings with up to second-nearest neighbor coupling embedded to a ring-shaped lead using exact diagonalization. The approach captures all the correlation effects and enables us to include interactions both in the ring and in the ring-shaped lead, and study on an equal footing weak and strong coupling between the ring and the lead as well as asymmetry. In the weakly coupled case, we find fractional periodicity at all electron fillings at sufficiently high Hubbard U, similar to isolated rings. For strongly coupled rings, on the contrary, fractional periodicity is only observed at sufficiently large negative gate voltages and high interaction strengths. This is explained by the formation of a bound correlated state in the ring that is effectively weakly coupled to the lead.