We consider the diffusive spin dynamics of a 2D electron gas with spin-orbit coupling confined within a grid of narrow channels. We show that the lifetime of certain spin distributions in such grids greatly exceeds that in an unconfined 2D electron gas and diverges as the channel width approaches zero. Such persistent spin grids are akin to spin crystals and occur if the electron spin orientation remains invariant after diffusion around the grid plaquette. We establish a topological ${\mathbb{Z}}_2$ classification for persistent spin grids and show how the grids with spatially varying parameters can simulate non-Abelian lattice gauge theories.

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• Non-Abelian gauge theories
• Spin diffusion
• Spin relaxation
• Spin-orbit coupling
• Nanostructures
• Quantum wells
• Two-dimensional electron gas
• Lattice gauge theory