  We study nonlinear Drude weights (NLDWs) for the spin-1/2 XXZ chain in the
critical regime at zero temperature. The NLDWs are generalizations of the
linear Drude weight. Via the nonlinear extension of the Kohn formula, they can
be read off from higher-order finite-size corrections to the ground-state
energy in the presence of a $U(1)$ magnetic flux. The analysis of the
ground-state energy based on the Bethe ansatz reveals that the NLDWs exhibit
convergence, power-law, and logarithmic divergence, depending on the anisotropy
parameter $\Delta$. We determine the convergent and power-law divergent
regions, which depend on the order of the response $n$. Then, we examine the
behavior of the NLDWs at the boundary between the two regions and find that
they converge for $n=0, 1, 2$ $({\rm mod}~4)$, while they show logarithmic
divergence for $n=3$ $({\rm mod}~4)$. Furthermore, we identify particular
anisotropies $\Delta=\cos(\pi r/(r+1))$ ($r=1,2, 3,\ldots$) at which the NLDW
at any order $n$ converges to a finite value.
