Thouless approach in transport in integrable and perturbed easy-axis Heisenberg chains

TL;DR

This paper investigates spin transport in integrable and perturbed easy-axis Heisenberg chains using the Thouless approach, revealing how integrability and perturbations influence transport properties and level sensitivity.

Contribution

It introduces the application of the Thouless approach to spin chains, demonstrating how integrability and perturbations affect transport and level sensitivity, with implications for conductivity behavior.

Findings

Integrable XXZ model shows diffusive transport but near-ballistic level sensitivity.

Perturbations reduce level sensitivity and induce a crossover to normal dissipative transport.

Spin conductivity exhibits a discontinuous jump proportional to perturbation strength.

Abstract

We study transport in spin chains employing the Thouless approach based on the level sensitivity to the boundary conditions, $R$. Although spin transport in the integrable easy-axis XXZ model is diffusive, corresponding $R$ is much closer to ballistic chains than to chaotic diffusive systems. In the case of the grand canonical ensemble, this observation can be rigorously justified, while in the case of the canonical ensemble it can be demonstrated by numerical calculations. Integrability breaking perturbation (IBP) strongly reduces $R$ which reveals a pronounced minimum at the crossover from anomalous diffusive to normal dissipative transport. This minimum coincides with the onset of the universality of the random matrix theory. Results for various IBP suggest a discontinuous jump of the spin conductivity in the thermodynamic limit, and moreover that its value is proportional to the strength of the IBP.