On the finite temperature Drude weight of the anisotropic Heisenberg   chain
  We present a study of the Drude weight $D(T)$ of the spin-1/2 $XXZ$ chain in the gapless regime. The thermodynamic Bethe ansatz (TBA) is applied in two different ways. In the first application we employ the particle basis of magnons and their bound states. In this case we rederive and considerably extend earlier work in the literature. However, in the course of our investigation we find arguments that cast doubt on the applicability of the TBA in this case. In a second application by use of the spinon and anti-spinon particle basis we obtain completely different results. Only for anisotropy parameter $\Delta$ close to 0 we find that $D(T)$ is a monotonously decaying function of temperature. For $\Delta$ close to 1 the behaviour is entirely different showing a finite temperature maximum. Also for the isotropic antiferromagnetic chain ($\Delta=1$) the results for $D(T)$ are finite for T=0 as well as for $T>0$ with an infinite positive slope at T=0. 
J. Benz, T. Fukui, A. Kl\"umper, C. Scheeren