# Kardar-Parisi-Zhang physics in the quantum Heisenberg magnet

## TL;DR

This paper demonstrates that the KPZ universality class describes magnetization dynamics in the quantum Heisenberg spin chain, revealing a new quantum analog of classical fluctuation phenomena.

## Contribution

It provides the first evidence of KPZ universality in a quantum many-body system, using novel theoretical and numerical methods.

## Key findings

- KPZ scaling function describes magnetization dynamics in the quantum Heisenberg chain
- Energy conservation does not influence KPZ physics in this quantum system
- Introduces new tools for analyzing quantum nonequilibrium correlations

## Abstract

Equilibrium spatio-temporal correlation functions are central to understanding weak nonequilibrium physics. In certain local one-dimensional classical systems with three conservation laws they show universal features. Namely, fluctuations around ballistically propagating sound modes can be described by the celebrated Kardar-Parisi-Zhang (KPZ) universality class. Can such universality class be found also in quantum systems? By unambiguously demonstrating that the KPZ scaling function describes magnetization dynamics in the SU(2) symmetric Heisenberg spin chain we show, for the first time, that this is so. We achieve that by introducing new theoretical and numerical tools, and make a puzzling observation that the conservation of energy does not seem to matter for the KPZ physics.