Kardar-Parisi-Zhang physics in integrable rotationally symmetric dynamics on discrete space-time lattice

TL;DR

This paper introduces an integrable, SO(3) invariant classical spin dynamics on a discrete lattice, demonstrating KPZ universality in spin transport through analytical and numerical methods.

Contribution

It presents a new integrable classical spin model with explicit solutions to the quantum Yang-Baxter equation and connects its dynamics to KPZ universality class.

Findings

Correlation functions follow KPZ scaling with dynamical exponent z=3/2

Model reduces to lattice Landau-Lifshitz in a continuous limit

Numerical simulations confirm KPZ universality in spin transport

Abstract

We introduce a deterministic SO(3) invariant dynamics of classical spins on a discrete space-time lattice and prove its complete integrability by explicitly finding a related non-constant (baxterized) solution of the set-theoretic quantum Yang-Baxter equation over the 2-sphere. Equipping the algebraic structure with the corresponding Lax operator we derive an infinite sequence of conserved quantities with local densities. The dynamics depend on a single continuous spectral parameter and reduce to a (lattice) Landau-Lifshitz model in the limit of a small parameter which corresponds to the continuous time limit. Using quasi-exact numerical simulations of deterministic dynamics and Monte Carlo sampling of initial conditions corresponding to a maximum entropy equilibrium state we determine spin-spin spatio-temporal (dynamical) correlation functions with relative accuracy of three orders of magnitude. We demonstrate that in the equilibrium state with a vanishing total magnetization the correlation function precisely follow Kardar-Parisi-Zhang scaling hence the spin transport belongs to the universality class with dynamical exponent z=3/2, in accordance to recent related simulations in discrete and continuous time quantum Heisenberg spin 1/2 chains.