Kinetic Theory of Spin Diffusion and Superdiffusion in XXZ Spin Chains

Area of Science:

• Condensed matter physics
• Quantum magnetism
• Statistical mechanics

Background:

• Spin transport in integrable quantum systems is complex.
• The Heisenberg limit of the XXZ spin chain is a key theoretical model.
• Previous numerical studies observed superdiffusion but lacked theoretical explanation.

Purpose of the Study:

• To theoretically explain the superdiffusive spin transport in the XXZ spin chain.
• To derive the diffusion constant in the isotropic Heisenberg limit.
• To analyze the behavior of spin transport in anisotropic XXZ models.

Main Methods:

• Utilizing a kinetic theory approach.
• Combining generalized hydrodynamics with Gaussian fluctuations.
• Applying a self-consistent treatment to account for divergences.

Main Results:

• The diffusion constant diverges in the Heisenberg limit.
• Superdiffusion is demonstrated with a time-dependent diffusion constant D(t) scaling as t^{1/3}.
• Closed-form expressions for the diffusion constant in anisotropic models (Δ>1) were derived.

Conclusions:

• The theoretical framework successfully explains previously observed superdiffusion exponents.
• Spin transport exhibits distinct behaviors in isotropic versus anisotropic XXZ models.
• The derived scaling laws provide valuable insights into quantum spin dynamics.