From dissipationless to normal diffusion in easy-axis Heisenberg spin chain

TL;DR

This paper investigates how introducing integrability-breaking perturbations in the easy-axis Heisenberg spin chain transitions spin transport from ballistic to normal diffusion, revealing a discontinuous change in the diffusion constant.

Contribution

It demonstrates that integrability-breaking perturbations cause a sudden shift from ballistic to diffusive spin transport, challenging the relevance of the integrable model's diffusion constant.

Findings

Ballistic transport is replaced by normal diffusion with perturbations.

The diffusion constant varies discontinuously with perturbation strength.

The integrable model's diffusion constant is not applicable for spin conductivity.

Abstract

The anomalous spin diffusion of the integrable easy-axis Heisenberg chain originates in the ballistic transport of symmetry sectors with nonzero magnetization. Ballistic transport is replaced by normal dissipative transport in all magnetization sectors upon introducing the integrability-breaking perturbations, including external driving. Such behavior implies that the diffusion constant obtained for the integrable model is relevant for the spread of spin excitations but not for the spin conductivity. We present numerical results for closed systems and driven open systems, indicating that the diffusion constant shows a discontinuous variation as the function of perturbation strength.