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

Abstract

Using the framework of generalized hydrodynamics, we compute here 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 method 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.