  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.
