Quantum fluctuation-induced uniaxial and biaxial spin nematics

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It is shown that zero point quantum fluctuations (ZPQFs) completely lift the accidental continuous degeneracy that is found in mean field analysis of quantum spin nematic phases of hyperfine spin 2 cold atoms. The result is two distinct ground states which have higher symmetries: a uniaxial spin nematic and a biaxial spin nematic with dihedral symmetry Dih₄. There is a novel first order quantum phase transition between the two phases as atomic scattering lengths are varied. We find that the ground state of ⁸⁷Rb atoms should be a uniaxial spin nematic. We note that the energy barrier between the phases could be observable in dynamical experiments.