Drude Weight at Finite Temperatures for Some Non-Integrable 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 non-vanishing, even when the system is {\it non-integrable} 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.