  Using the Bethe ansatz method and the TBA equations for the higher spin
integrable XXZ chain, the regular zero frequency contribution to the spin
current correlation (spin dc conductivity) is analyzed for the spin-1/2 XXZ
chain with an anisotropy $0 \le \Delta <1$. In the high temperature limit, we
write down the dressed scattering kernels by one quasi-particle bare energies,
which allows the exact evaluation of the infinite temperature spin dc
conductivity $\mathcal{L}$. We find that $\mathcal{L}$ is discontinuous at all
rational numbers of the anisotropy parameter $p_0=\pi/\cos^{-1}\Delta$ in the
region $p_0 \ge 2$ with the gap increasing larger than the second power of
growing magnetization on one quasi-particle. The isotropic $\Delta=1$ point is
exceptional. Close to this point, $\mathcal{L}$ slowly increases in proportion
to the first power of the magnetization. On the other hand $\mathcal{L}$ is
proportional to the second power of the magnetization when $p_0$ approaches
irrational numbers.
