Quantum phases of the Shraiman-Siggia model

We examine phases of the Shraiman-Siggia model of lightly doped, square lattice quantum antiferromagnets in a self-consistent, two-loop, interacting magnon analysis. We find magnetically ordered and quantum-disordered phases both with and without incommensurate spin correlations. The quantum-disordered phases have a pseudogap in the spin excitation spectrum. The quantum transition between the magnetically ordered and commensurate quantum-disordered phases is argued to have the dynamic critical exponent z=1 and the same leading critical behavior as the disordering transition in the pure O (3) model. The relationship to experiments on the doped cuprates is discussed.