In this talk, I will review some recent theoretical results of spincorrelated ultra cold atoms in optical lattices or traps. Spin correlated
physics ofsodium, rubidium, chromium atoms has attracted a lot of attentionrecently and in quite a few cases quantum spin nematics have been foundto be ground states. I will discuss the nature of various quantum spinnematics, and fractionalized vortices (1/2-, and 1/3-quantum vortices)that are unique in spin-nematic superfluids. Quantum phase transitionsbetween various spin correlated states will also be briefly addressed. Atthe end, I will discuss quantum fluctuation-induced uniaxial and biaxialnematics of hyperfine spin two cold atoms and dynamics of rubidium-87
atoms.
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