Scaling of diffusion constants in perturbed easy-axis Heisenberg spin chains

TL;DR

This paper investigates how diffusion constants in perturbed easy-axis Heisenberg spin chains change under integrability-breaking conditions, using various methods to analyze both closed and open systems and revealing a continuous variation and potential divergence of diffusion constants.

Contribution

It provides a comprehensive analysis of diffusion constant behavior in perturbed easy-axis Heisenberg chains, combining multiple approaches to reveal their continuous change and possible divergence.

Findings

Diffusion constants vary continuously with perturbation strength.

Agreement between closed and open system results in certain regimes.

Potential divergence of diffusion constant in open systems at weak perturbations.

Abstract

Understanding the physics of the integrable spin-1/2 XXZ chain has witnessed substantial progress, due to the development and application of sophisticated analytical and numerical techniques. In particular, infinite-temperature magnetization transport has turned out to range from ballistic, over superdiffusive, to diffusive behavior in different parameter regimes of the anisotropy. Since integrability is rather the exception than the rule, a crucial question is the change of transport under integrability-breaking perturbations. This question includes the stability of superdiffusion at the isotropic point and the change of diffusion constants in the easy-axis regime. In our work, we study this change of diffusion constants by a variety of methods and cover both, linear response theory in the closed system and the Lindblad equation in the open system, where we throughout focus on periodic boundary conditions. In the closed system, we compare results from the recursion method to calculations for finite systems and find evidence for a continuous change of diffusion constants over the full range of perturbation strengths. In the open system weakly coupled to baths, we find diffusion constants in quantitative agreement with the ones in the closed system in a range of nonweak perturbations, but disagreement in the limit of weak perturbations. Using a simple model in this limit, we point out the possibility of a diverging diffusion constant in such an open system.