Infinite temperature spin dc conductivity of the spin-1/2 XXZ chain

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.