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 time scale for the onset of diffusion, albeit with uncertainty over the exact scaling exponent. That is, for perturbations of strength λ, the characteristic timescale for diffusion goes as t*∼λ−α for some α. 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 [McCarthy , Phys. Rev. B 110, L180301 (2024)2469-995010.1103/PhysRevB.110.L180301]: α=2 for symmetry-breaking terms and α=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 α=6 scaling appears to be universal across superdiffusive systems when the perturbations preserve the non-Abelian symmetry G.