Anisotropic spin models can have exact symmetry groups outside O(3)xIsom(R^3), enforced by cohomology twists, and can host Z2 quadrupolar excitations on a spin Brillouin Klein bottle.
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On the Symmetries of Anisotropic Spin Interaction Models
Anisotropic spin models can have exact symmetry groups outside O(3)xIsom(R^3), enforced by cohomology twists, and can host Z2 quadrupolar excitations on a spin Brillouin Klein bottle.