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

Abstract

In the easy-plane regime of XXZ spin chains, spin transport is ballistic, with a Drude weight that has a discontinuous fractal dependence on the value of the anisotropy $\hat{I}”=\cos \ddot{I}€\hat{I}»$ at nonzero temperatures. We show that this structure necessarily implies the divergence of the low-frequency conductivity for generic irrational values of $\hat{I}»$. Within the framework of generalized hydrodynamics, we show that in the high-temperature limit the low-frequency conductivity at a generic anisotropy scales as $\ddot{I}ƒ(\ddot{I}‰)\sim 1/\sqrt{\ddot{I}}‰$; anomalous response occurs because quasiparticles undergo Lévy flights. For rational values of $\hat{I}»$, the divergence is cut off at low frequencies and the corrections to ballistic spin transport are diffusive. We also use our approach to recover that at the isotropic point $\hat{I}”=1$, spin transport is superdiffusive with $\ddot{I}ƒ(\ddot{I}‰)\sim \ddot{I}{‰}^{-1/3}$. We support our results with extensive numerical studies using matrix-product operator methods.

5pp, 2 figs, plus supplemental material