Anomalous low-frequency conductivity in easy-plane XXZ spin chains

Using the framework of generalized hydrodynamics, we compute the low-frequency spin conductivity σ(ω) of XXZ spin chains with easy-plane anisotropy. We find that for almost all values of the anisotropy-1<Δ<1, the low-frequency conductivity scales anomalously with frequency, as σ(ω)∼1/ω. We interpret this anomalous response as a consequence of quasiparticles undergoing Lévy flights. For special values of the anisotropy, the divergence is cut off at low frequencies, so σ(ω) has a finite dc limit. These results reveal a hitherto unknown mechanism for anomalous response in integrable systems and also provide a physical explanation of the discontinuous behavior of the spin Drude weight. We use our approach to recover that at the isotropic point Δ=1, σ(ω)∼ω-1/3. We support our results with extensive numerical studies using matrix-product operator methods.