Imambekov, AdiletLukin, MikhailDemler, Eugene2016-08-252003Imambekov, Adilet, Mikhail Lukin, and Eugene Demler. 2003. “Spin-Exchange Interactions of Spin-One Bosons in Optical Lattices: Singlet, Nematic, and Dimerized Phases.” Physical Review A 68 (6) (December 4). doi:10.1103/physreva.68.063602.1050-2947http://nrs.harvard.edu/urn-3:HUL.InstRepos:27945412We consider insulating phases of cold spin-1 bosonic particles with antiferromagnetic interactions, such as 23Na, in optical lattices. We show that spin-exchange interactions give rise to several distinct phases, which differ in their spin correlations. In two- and three-dimensional lattices, insulating phases with an odd number of particles per site are always nematic. For insulating states with an even number of particles per site, there is always a spin-singlet phase, and there may also be a first-order transition into the nematic phase. The nematic phase breaks spin rotational symmetry but preserves time reversal symmetry, and has gapless spin-wave excitations. The spin-singlet phase does not break spin symmetry and has a gap to all excitations. In one dimensional lattices, insulating phases with an odd number of particles per site always have a regime where translational symmetry is broken and the ground state is dimerized. We discuss signatures of various phases in Bragg scattering and time-of-flight measurements.en-USJournal Article2016-08-2510.1103/physreva.68.063602