# Kardar-Parisi-Zhang Scaling for an Integrable Lattice Landau-Lifshitz Spin Chain

## TL;DR

This paper investigates the scaling behavior of an integrable lattice Landau-Lifshitz spin chain, revealing KPZ universality in the zero magnetization case and contrasting transport regimes across different parameters.

## Contribution

It demonstrates that the equilibrium correlations in the zero magnetization case follow KPZ scaling, extending understanding of anomalous transport in integrable spin chains.

## Key findings

- KPZ scaling function matches that of the stochastic Burgers equation.
- Ballistic transport observed in easy-plane regime.
- Diffusive transport observed in easy-axis regime.

## Abstract

Recent studies report on anomalous spin transport for the integrable Heisenberg spin chain at its isotropic point. Anomalous scaling is also observed in the time-evolution of non-equilibrium initial conditions, the decay of current-current correlations, and non-equilibrium steady state averages. These studies indicate a space-time scaling with $x \sim t^{2/3}$ behavior at the isotropic point, in sharp contrast to the ballistic form $x \sim t$ generically expected for integrable systems. In our contribution we study the scaling behavior for the integrable lattice Landau-Lifshitz spin chain. We report on equilibrium spatio-temporal correlations and dynamics with step initial conditions. Remarkably, for the case with zero mean magnetization, we find strong evidence that the scaling function is identical to the one obtained from the stationary stochastic Burgers equation, alias Kardar-Parisi-Zhang equation. In addition, we present results for the easy-plane and easy-axis regimes for which, respectively, ballistic and diffusive spin transport is observed, whereas the energy remains ballistic over the entire parameter regime.