Uniaxial and biaxial spin nematic phases induced by quantum fluctuations

It is shown that zero point quantum fluctuations 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.