Kubo's response theory and bosonization with a background gauge field and irrelevant perturbations

Using conformal field theory calculations of the energy spectrum, within XXZ model we investigate effects flux insertion and Umklapp term. We discuss two approaches to evaluation Drude weight, first corresponding linear response second twisted boson with Divergences obtained in context former contradict Bethe ansatz results, coinciding for free fermion point only. The origin this discrepancy is different order which term are treated, where marginal perturbation should be considered before irrelevant. calculate scaling conductivity system size temperature long-wave limit.