Anomalous transport in perturbed Heisenberg chain

We study high-temperature transport in quantum chains, at and away from integrability. Using a set of exact sum-rule moment relations, memory function Ansatz, and exact diagonalization we investigate the response of the integrable XXZ model to next-nearest neighbour integrability breaking spin-flips. In the integrable model we find a panoply of transport rates as the interactions are tuned: subleading subballistic, superdiffusive, and normal diffusion. We further find the sign of the integrability breaking perturbation matters: while positive spin-flips (in-plane frustration in the ground state) enhance spin transport, there is a narrow interval of negative spin-flip amplitudes for which transport is strongly suppressed. The resulting (anomalous) long-time transport tails as inferred from the regular conductivity of small spin chains are captured faithfully, qualitatively and quantitatively, by the memory function Ansatz in all regimes: gapless, isotropic, and gapped for the integrable chain, as well as across vast parametric swathes of the nonintegrable chain. In sharp contrast, the asymmetry with respect to the sign of the perturbation is absent in the fermionic analog of the model, which is also captured nicely by this hybrid memory function approach.