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We present a general approach to understanding the quantum phases and phasetransitions of quantum antiferromagnets in two spatial dimensions. We beginwith the simplest spin liquid state, the Z_2 spin liquid, whose elementaryexcitations are spinons and visons, carrying Z_2 electric and magnetic chargesrespectively. Their dynamics are expressed in terms of a doubled U(1)Chern-Simons theory, which correctly captures the `topological' order of theZ_2 spin liquid state. We show that the same theory also yields a descriptionof the variety of ordered phases obtained when one or more of the elementaryexcitations condense. Field theories for the transitions and multicriticalpoints between these phases are obtained. We also survey experimental resultson antiferromagnets on the anisotropic triangular lattice, and make connectionsbetween their phase diagrams and our results.

Global phase diagrams of frustrated quantum antiferromagnets in two dimensions: doubled Chern-Simons theory