Breakdown of superdiffusion in perturbed quantum integrable spin chains and ladders

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 timescale 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 $SU(2)$ symmetry, leading to scaling exponents consistent with those observed in one classical study arXiv:2402.18661: $\alpha=2$ for symmetry-breaking terms and $\alpha=6$ for symmetry-preserving terms. We also consider perturbations from another integrable point of the ladder model with $G=SU(4)$ and find consistent results. Finally, we consider a generalization to an $SU(3)$ ladder and find that the $\alpha=6$ scaling appears to be universal across superdiffusive systems when the perturbations preserve the non-abelian symmetry $G$.