The S=1/2 XY and XYZ models on d≥2 hypercubic lattices possess no nontrivial local conserved quantities.
Takahashi, Thermodynamics of One-Dimensional Solvable Models , (Cambridge Uni- versity Press, 2005)
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The quantum compass model on the square lattice possesses no nontrivial local conserved quantities besides the Hamiltonian.
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The $S=\frac{1}{2}$ XY and XYZ models on the two or higher dimensional hypercubic lattice do not possess nontrivial local conserved quantities
The S=1/2 XY and XYZ models on d≥2 hypercubic lattices possess no nontrivial local conserved quantities.