Infinite temperature transport in the strong coupling regime of a nonintegrable quantum spin chain

We study spin transport of the XXZ model with next-nearest neighbor $\Delta_2$ terms. We compute numerically dependence of spin conductivity $\sigma(\omega)$ on the anisotropy $\Delta$ and the ratio $r= \Delta_2/\Delta$, in the large $\Delta$ regime. We find that, when $0<r<1$, the low-frequency conductivity assumes an anomalous form $\sigma(\omega)\approx a \omega^2 + b \Delta^{-2}$. In particular, when $\Delta\to\infty$ the model becomes dynamically constrained and most states are localized. We show, microscopically, existence of magnon bound states in the strong coupling regime, which behave as self-generated disorders for single magnons. Based on this quasiparticle picture, we obtain analytical scalings, which match well with the numerical results.