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.

Figure 1

Plot of $D(T)$ vs $T$ for ${\beta }^2=1$, $1/12$, $1/8$, $5/6$, $3/5$ (from bottom to top). For comparison, the QMC data for ${\beta }^2=5/6$ is quoted from Ref. 10 (circles).