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The spin element of the Onsager matrix for the spin-$\frac{1}{2}$ criticalXXZ chain at infinite temperature and zero magnetic field is studied toevaluate the spin diffusion. Its formula is written down by known functionswith the use of TBA equations for the integrable XXZ chain with arbitrary spin.We treat the element of the Onsager matrix as a function of the anisotropyparameter $\Delta=\cos\theta$ where $\frac{\theta}{\pi}$ is a rational number.The element shows a popcorn dependence on the $\Delta$ in a way it isdiscontinuous at every parametrized point. Moreover the element diverges at allthe discontinuous points.

Spin element of Onsager matrix for spin-$\frac{1}{2}$ critical XXZ chain at infinite temperature and zero magnetic field