Abstract
Using the framework of generalized hydrodynamics, we compute the low-frequency spin conductivity of XXZ spin chains with easy-plane anisotropy. We find that for almost all values of the anisotropy , the low-frequency conductivity scales anomalously with frequency, as . 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 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 , . We support our results with extensive numerical studies using matrix-product operator methods.
- Received 20 September 2019
- Revised 23 January 2020
- Accepted 12 May 2020
DOI:https://doi.org/10.1103/PhysRevB.101.224415
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