Graphene SU(4) quantum Hall symmetry is extended to SO(8), permitting analytical solutions for graphene in a magnetic field that break SU(4) spontaneously. We recover standard graphene SU(4) physics as one limit, but find new phases and new properties that may be relevant for understanding the ground state. The graphene SO(8) symmetry is found to be isomorphic to one that occurs extensively in nuclear structure physics, and very similar to one that describes high-temperature superconductors, suggesting deep mathematical connections among these physically-different fermionic systems.
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