# Anomalous spin diffusion in one-dimensional antiferromagnets

## TL;DR

This paper investigates low-temperature spin dynamics in one-dimensional antiferromagnetic chains, revealing super-diffusive behavior and universality class characteristics through a combination of theoretical analysis and numerical simulations.

## Contribution

It introduces an exact non-perturbative approach to analyze spin transport near non-magnetized states, uncovering anomalous super-diffusive behavior and universality class features.

## Key findings

- Discovery of super-diffusive spin transport near half-filling.
- Identification of Kardar-Parisi-Zhang universality class for spin fluctuations.
- Evidence of anomalous transport persisting at high temperatures.

## Abstract

The problem of characterizing low-temperature spin dynamics in antiferromagnetic spin chains has so far remained elusive. We reinvestigate it by focusing on isotropic antiferromagnetic chains whose low-energy effective field theory is governed by the quantum non-linear sigma model. We outline an exact non-perturbative theoretical approach to analyse the low-temperature behaviour in the vicinity of non-magnetized states, and obtain explicit expressions for the spin diffusion constant and the NMR relaxation rate, which we compare with previous theoretical results in the literature. Surprisingly, in SU(2)-invariant spin chains in the vicinity of half-filling we find a crossover from the semi-classical regime to a strongly interacting quantum regime characterized by zero spin Drude weight and diverging spin conductivity, indicating super-diffusive spin dynamics. The dynamical exponent of spin fluctuations is argued to belong to the Kardar-Parisi-Zhang universality class. Furthermore, by employing numerical tDMRG simulations, we find robust evidence that the anomalous spin transport persists also at high temperatures, irrespectively of the spectral gap and integrability of the model.