A Schwinger boson mean field study of the $J_1$-$J_2$ Heisenberg triangular-lattice quantum antiferromagnet

We use Schwinger boson mean field theory to study the ground state of the spin-$S$ triangular-lattice Heisenberg model with nearest ($J_1$) and next-nearest ($J_2$) neighbor antiferromagnetic interactions, treating $\kappa=2S$ as a continuous parameter. We consider two spin liquid Ansatze whose magnetically ordered versions correspond to 120-degree order and a a collinear ''stripe" order, respectively. For $\kappa=1$ there is a direct transition between these ordered states as $J_2/J_1$ increases. Motivated by an argument that a smaller $\kappa$ may be more appropriate for describing the $S=1/2$ case qualitatively, we find that as one lowers $\kappa$, a spin liquid region eventually opens up between the ordered phases, in qualitative agreement with various recent numerical studies of the $S=1/2$ model. This picture suggests a symmetric gapped Z$_2$ spin liquid which is the disordered version of the 120-degree ordered state.