Features of spin-charge separation in the equilibrium conductance through finite rings

We calculate the conductance through rings with few sites $L$ described by the $t-J$ model, threaded by a magnetic flux $Phi$ and weakly coupled to conducting leads at two arbitrary sites. The model can describe a circular array of quantum dots with large charging energy $U$ in comparison with the nearest-neighbor hopping $t$. We determine analytically the particular values of $Phi$ for which a depression of the transmittance is expected as a consequence of spin-charge separation. We show numerically that the equilibrium conductance at zero temperature is depressed at those particular values of $Phi $ for most systems, in particular at half filling, which might be easier to realize experimentally.