Transport in a class of exactly solvable models of interacting fermions

We study transport in a class of exactly solvable models of interacting fermions in one dimension. We contrast these models with models of non-interacting fermions in an Aharanov-Bohm ring to which they are superficially similar. We introduce magnetic and non-magnetic impurities at a site, through either a weak $\delta$-function potential or through a weak link. Using a renormalisation group analysis, we show that the strength of the nonmagnetic impurity is not affected by the interaction, whereas the magnetic impurity cuts the wire at the impurity site.