Kavli Affiliate: Joel E. Moore
| First 5 Authors: Kevin Wang, Joel E. Moore, , ,
| Summary:
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 $G$.
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