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

We present a general approach to understanding the quantum phases and phase transitions of quantum antiferromagnets in two spatial dimensions. We begin with the simplest spin-liquid state, the Z₂ spin liquid, whose elementary excitations are spinons and visons, carrying Z₂ electric and magnetic charges, respectively. Their dynamics is expressed in terms of a doubled U(1) Chern-Simons theory, which correctly captures the ``topological'' order of the Z₂ spin-liquid state. We show that the same theory also yields a description of the variety of ordered phases obtained when one or more of the elementary excitations condense. Field theories for the transitions and multicritical points between these phases are obtained. We survey experimental results on antiferromagnets on the anisotropic triangular lattice, and make connections between their phase diagrams and our results.