Fig. 5.

Classical kinetically constrained models. Structure factor $\mathcal{C}(x,t)=\langle {\sigma }^z(x,t){\sigma }^z(0,0)\rangle$ in a stochastic model with charge and domain wall conservation, with local interactions (nonunitary “gates”) acting on M sites. For M = 4, which is the case relevant to the XXZ spin chain with broken integrability, the magnon number is conserved, and we find subdiffusive transport with z = 4 (Left). For higher-range interactions, the magnon number is not conserved, and we find ordinary diffusion z = 2, indicating that domain wall conservation is not enough for subdiffusion to occur.