Macroscopic Diffusive Transport in a Microscopically Integrable Hamiltonian System

TL;DR

This paper shows that a classical integrable spin chain exhibits diffusive or ballistic transport depending on the regime, challenging previous assumptions and suggesting new conservation laws in integrable systems.

Contribution

It reveals diffusive spin transport in an integrable classical model and suggests the existence of novel quasi-local conservation laws beyond known soliton theory.

Findings

Diffusive transport with finite diffusion constant in the easy-axis regime.

Ballistic transport in the easy-plane regime.

Implication of new quasi-local conservation laws.

Abstract

We demonstrate that a completely integrable classical mechanical model, namely the lattice Landau-Lifshitz classical spin chain, supports diffusive spin transport with a finite diffusion constant in the easy-axis regime, while in the easy-plane regime it displays ballistic transport in the absence of any known relevant local or quasi-local constant of motion in the symmetry sector of the spin current. This surprising finding should open the way towards analytical computation of diffusion constants for integrable interacting systems and hints on existence of new quasi-local classical conservation laws beyond the standard soliton theory.