Symmetry breaking Schwinger Boson Mean Field Theory solutions on Kagome

Schwinger Boson Mean Field theory (SBMFT) is a powerful technique for describing both quantum disordered and symmetry broken phases of Heisenberg spins as a function of spin length $\kappa=2S$. Previous applications of SBMFT have been to study \emph{symmetric} SL's which preserve lattice and time reversal symmetries (TRS). The \emph{assumption} of a symmetric ground state reduces the number of mean field variables simplifying search for SL saddle points. We go beyond the manifold of \emph{symmetric} SL's on the kagome lattice and using an optimization \footnote{G.Misguich, PRB 86, 245132 (2012)} technique search for solutions that may \emph{spontaneously} break lattice and TRS. An exhaustive search for saddle points on a $4\times4$ lattice shows that the lowest energy solutions have zero flux ($[0hex]$) through hexagons in agreement with the Greedy Boson theorem \footnote{O. Tchernyshyov et al. EPL, 73, 278 (2006)} However, amongst the manifold of $[0hex]$ solutions we find a state \emph{lower} in energy than Sachdev's uniform $Q_{1}=-Q_{2}$ state, extending up to $\kappa=0.3$, which \emph{spontaneously} breaks lattice symmetry and differs from uniform solution in flux patterns through length eight loops . We also characterize other (higher in energy) \emph{chiral} saddle points