# Universal spin dynamics in infinite-temperature one-dimensional quantum magnets

## TL;DR

This paper uncovers universal spin transport regimes in one-dimensional quantum magnets at infinite temperature, revealing superdiffusive, ballistic, and diffusive behaviors across various models using advanced tensor network simulations.

## Contribution

It identifies three universal spin transport regimes in quantum spin chains, extending understanding beyond the well-studied $S=1/2$ Heisenberg model, and clarifies their relation to integrability and symmetries.

## Key findings

- Superdiffusive transport with $z=3/2$ in integrable models with extra symmetries.
- Ballistic transport with $z=1$ in integrable models with finite Drude weight.
- Diffusive transport with $z=2$ in non-integrable or anisotropic models.

## Abstract

We address the nature of spin dynamics in various integrable and non-integrable, isotropic and anisotropic quantum spin-$S$ chains, beyond the paradigmatic $S=1/2$ Heisenberg model. In particular, we investigate the algebraic long-time decay $\propto t^{-1/z}$ of the spin-spin correlation function at infinite temperature, using state-of-the-art simulations based on tensor network methods. We identify three universal regimes for the spin transport, independent of the exact microscopic model: (i) superdiffusive with $z=3/2$, as in the Kardar-Parisi-Zhang universality class, when the model is integrable with extra symmetries such as spin isotropy that drive the Drude weight to zero, (ii) ballistic with $z=1$ when the model is integrable with a finite Drude weight, and (iii) diffusive with $z=2$ with easy-axis anisotropy or without integrability, at variance with previous observations.