Superdiffusive transport with dynamical exponent $z=3/2$ has been firmly established at finite temperature for a class of integrable systems with a non-Abelian global symmetry $G$. On the inclusion of integrability-breaking perturbations, diffusive transport with $z=2$ is generically expected to hold in the limit of late time. Recent studies of the classical Haldane-Ishimori-Skylanin model have found that perturbations that preserve the global symmetry lead to a much slower time scale for the onset of diffusion, albeit with uncertainty over the exact scaling exponent. That is, for perturbations of strength $\lambda$, the characteristic timescale for diffusion goes as $t_{*}\sim {\lambda }^{-\alpha }$ for some $\alpha$. Using large-scale matrix product state simulations, we investigate this behavior for perturbations to the canonical quantum model showing superdiffusion: the $S=1/2$ quantum Heisenberg chain. We consider a ladder configuration and look at various perturbations that either break or preserve the $SU\left(2\right)$ symmetry, leading to scaling exponents consistent with those observed in one classical study [McCarthy et al., Phys. Rev. B 110, L180301 (2024)]: $\alpha =2$ for symmetry-breaking terms and $\alpha =6$ for symmetry-preserving terms. We also consider perturbations from another integrable point of the ladder model with $G=SU\left(4\right)$ and find consistent results. Finally, we consider a generalization to an $SU\left(3\right)$ ladder and find that the $\alpha =6$ scaling appears to be universal across superdiffusive systems when the perturbations preserve the non-Abelian symmetry $G$.

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• Anomalous diffusion
• Diffusion
• Transport phenomena
• Hydrodynamics
• Integrable systems
• Matrix product states
• Quantum spin chains
• Spin ladders