Drude weight at finite temperatures for some nonintegrable quantum systems in one dimension

Using conformal perturbation theory, we show that, for some classes of the one-dimensional quantum liquids that possess the Luttinger liquid fixed point in the low-energy limit, the Drude weight at finite temperatures is nonvanishing, even when the system is nonintegrable and the total current is not conserved. We also obtain the asymptotically exact low-temperature formula of the Drude weight for Heisenberg XXZ spin chains, which agrees quite well with recent numerical data.