The understanding of the physics of the integrable $\mathrm{spin}\text{−}1/2$ 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 in transport under integrability-breaking perturbations. This question includes the stability of superdiffusion at the isotropic point and the change in diffusion constants in the easy-axis regime. In our work, we study this change in diffusion constants using a variety of methods and cover both linear response theory in the closed system and the Lindblad equation in the open system, where we focus on periodic boundary conditions throughout. In the closed system, we compare results from the recursion method to calculations for finite systems and find evidence of a continuous change in 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 of this limit, we point out the possibility of a diverging diffusion constant in such an open system.

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• Nonequilibrium statistical mechanics
• Open quantum systems
• Quantum transport
• 1-dimensional spin chains
• Quantum many-body systems
• Heisenberg model
• Integrable systems
• Lindblad equation
• Quantum spin chains