We present a combined theory-experiment study to quantify spin diffusion in the square lattice quantum spin-$1/2$ XY model at finite temperature. On the theory side, we leverage a recently developed dynamical high-temperature expansion method to faithfully capture the long spatiotemporal scales of the hydrodynamic regime. Experimental results are obtained from an optical lattice hard-core boson quantum simulator. The excellent agreement of spin diffusion constants marks a breakthrough in spin transport beyond one dimension and for the quantitative validation of state-of-the-art quantum simulation platforms. We also provide theory predictions for future experiments on dynamic spin conductivity or anisotropy-induced integrability breaking.

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• Cold atoms & matter waves
• Cold gases in optical lattices
• Spin diffusion
• Perturbation theory