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We consider a model of one dimensional spin-1 bosons with repulsivedensity-density interactions and antiferromagnetic exchange. We show that thelow energy effective field theory is given by a spin-charge separated theory ofa Tomonaga-Luttinger Hamiltonian and the O(3) nonlinear sigma model describingcollective charge and spin excitations respectively. At a particular ratio ofthe density-density to spin-spin interaction the model is integrable, and weuse the exact solutions to provide an independent derivation of the low energyeffective theory. The system is in a superfluid phase made of singlet pairs ofbosons, and we calculate the long-distance asymptotics of certain correlationfunctions.

On the spin-liquid phase of one dimensional spin-1 bosons