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 pseudo-gap 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) sigma model. The relationship to experiments on the doped cuprates is discussed. Typeset using REVTEX