Broken Symmetries and Gapless Excitations of SU(N) Antiferromagnets Investigated With Variational Wavefunctions

We use Gutzwiller-projected wavefunctions to investigate variationally the phase diagrams of SU(N) quantum antiferromagnets in the self-conjugate representation. The method is first tested against the known phase diagram of a one-dimensional SU(4) bilinear-biquadratic spin chain which has a quantum-critical point separating a dimerized phase from a phase with spontaneously broken charge-conjugation symmetry\footnote{I. Affleck {\it et al.}, Nucl. Phys. B {\bf 366}, 467 (1991).}. In the case of two-dimensional SU(N) antiferromagnets, recent analytical\footnote{M. Hermele {\it et al.}, \urllink{cond-mat/0404751}{http://arxiv.org/abs/cond-mat/0404751}.} and numerical\footnote{F. F. Assaad, \urllink{cond-mat/0406074}{http://arxiv.org/abs/cond-mat/0406074}.} work suggests the existence of a gapless spin-liquid phase with no broken symmetries. Such a phase would be consistent with a recent generalization of the Lieb-Schultz-Mattis theorem\footnote{M. B. Hastings, Phys. Rev. B{\bf 69}, 104431 (2004); \urllink{cond-mat/0411094}{http://arxiv.org/abs/cond-mat/0411094}.} to more than one spatial dimension. We examine the stability of the $\pi$-flux phase against tendencies to spin-order, crystallize into various valence-bond solids, or break charge-conjugation symmetry.