Research Seminar - Kevin Wang

Abstract

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, which includes the Heisenberg chain, a canonical model of quantum magnetism. 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 a classical 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 λ, the characteristic timescale for diffusion scales as t ~ λ^{−α} for some α. Using large-scale matrix product state simulations, we investigate this behavior for perturbations to the S = 1/2 quantum Heisenberg chain, which is a good description for many quasi-1D magnetic systems. 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: 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.