One-dimensional strongly interacting electrons with a single impurity: Conductance reemergence

We show that the conductance of a 1D channel with one point-like impurity critically depends on the asymptotic behavior of the e-e interaction at low momenta k (about the inverse length of the channel). The conductance reemerges (contrary to the case of a point-like repulsive potential) if the potential satisfies the condition V (k = 0) = 0. For example, this happens if the bare e-e interaction is screened by the charges in the bulk. The relation of this phenomenon to the long-range order present in the Luttinger model is discussed. We consider spinless electrons but generalization is straightforward.