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

TL;DR

This paper investigates the anomalous low-frequency conductivity in easy-plane XXZ spin chains, revealing fractal dependence, divergence at irrational anisotropies, and superdiffusive behavior at the isotropic point, supported by numerical simulations.

Contribution

It demonstrates that low-frequency conductivity diverges for irrational anisotropies and exhibits superdiffusive behavior at the isotropic point, using generalized hydrodynamics and numerical methods.

Findings

Conductivity diverges as 1/√ω for irrational anisotropies.

At the isotropic point, spin transport is superdiffusive with σ(ω) ∼ ω^{-1/3}.

Numerical studies support the analytical predictions.

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 $\Delta = \cos \pi \lambda$ at nonzero temperatures. We show that this structure necessarily implies the divergence of the low-frequency conductivity for generic irrational values of $\lambda$. Within the framework of generalized hydrodynamics, we show that in the high-temperature limit the low-frequency conductivity at a generic anisotropy scales as $\sigma(\omega) \sim 1/\sqrt{\omega}$; anomalous response occurs because quasiparticles undergo L\'evy flights. For rational values of $\lambda$, 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 $\Delta=1$, spin transport is superdiffusive with $\sigma(\omega) \sim \omega^{-1/3}$. We support our results with extensive numerical studies using matrix-product operator methods.