# Magnetization dynamics in clean and disordered spin-1 XXZ chains

## TL;DR

This study investigates spin transport in the one-dimensional spin-1 XXZ chain at high temperatures, revealing diffusive behavior in the easy-axis regime and potential signs of many-body localization under disorder.

## Contribution

It provides a comprehensive numerical analysis of high-temperature spin transport in the spin-1 XXZ chain, highlighting diffusive dynamics and the effects of disorder, which were not fully understood before.

## Key findings

- High-temperature spin transport is diffusive in the easy-axis regime.
- Signatures of diffusion can persist at lower temperatures.
- Disorder induces a breakdown of diffusion and may lead to many-body localization.

## Abstract

We study spin transport in the one-dimensional anisotropic S = 1 Heisenberg model. Particular emphasis is given to dynamics at infinite temperature, where current autocorrelations and spatio-temporal correlation functions are obtained by means of an efficient pure-state approach based on the concept of typicality. Our comprehensive numerical analysis unveils that high-temperature spin transport is diffusive in the easy-axis regime for strong exchange anisotropies. This finding is based on the combination of numerous signatures, such as (i) Gaussian spreading of correlations, (ii) a time-independent diffusion coefficient, (iii) power-law decay of equal-site correlations, (iv) exponentially decaying long-wavelength modes, and (v) Lorentzian line shapes of the dynamical structure factor. Moreover, we provide evidence that some of these signatures are not exclusively restricted to the infinite-temperature limit, but can persist at lower temperatures as well, where we complement our results by additional quantum Monte Carlo simulations of large systems. In contrast to the easy-axis regime, we show that in the case of an isotropic chain, the signatures (i) - (v) are much less pronounced or even entirely absent, suggesting the existence of anomalous spin transport despite the nonintegrability of the model. Eventually, upon introducing a random on-site magnetic field, we observe a breakdown of diffusion and distinctly slower dynamics. In particular, our results exhibit qualitative similarities to disordered spin-1/2 chains and might be consistent with the onset of many-body localization in the S = 1 model for sufficiently strong disorder.