Barnett, RyanTurner, AriDemler, Eugene2016-08-242006Barnett, Ryan, Ari Turner, and Eugene Demler. 2006. “Classifying Novel Phases of Spinor Atoms.” Physical Review Letters 97 (18) (November 3). doi:10.1103/physrevlett.97.180412.0031-9007http://nrs.harvard.edu/urn-3:HUL.InstRepos:27893056We consider many-body states of bosonic spinor atoms which, at the mean-field level, can be characterized by a single-particle wave function for the Bose-Einstein condensation and Mott insulating states. We describe and apply a classification scheme that makes explicit the spin symmetries of such states and enables one to naturally analyze their collective modes and topological excitations. Quite generally, the method allows classification of a spin F system as a polyhedron with 2F vertices. We apply the method to the many-body states of bosons with spins two and three. For spin-two atoms we find the ferromagnetic state, a continuum of nematic states, and a state having the symmetry of the point group of the regular tetrahedron. For spin-three atoms we obtain similar ferromagnetic and nematic phases as well as states having symmetries of various types of polyhedra with six vertices.en-USJournal Article2016-08-2410.1103/PhysRevLett.97.180412