Schwinger boson mean field study of the \(J_1\)-\(J_2\) Heisenberg quantum antiferromagnet on the triangular lattice

We use Schwinger boson mean field theory (SBMFT) 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. Previous work on the \(S=1/2\) model leads us to consider two spin liquid Ans\"{a}tze, one symmetric and one nematic, which upon spinon condensation give magnetically ordered states with 120\(^{\circ}\) order and collinear stripe order, respectively. The SBMFT contains the parameter \(\kappa\), the expectation value of the number of bosons per site, which in the exact theory equals \(2S\). For \(\kappa=1\) there is a direct, first-order transition between the ordered states as \(J_2/J_1\) increases. Motivated by arguments that in SBMFT, smaller \(\kappa\) may be more appropriate for describing the \(S=1/2\) case qualitatively, we find that in a \(\kappa\) window around 0.6, a region with the (gapped \(Z_2\)) symmetric spin liquid opens up between the ordered states. As a consequence, the static structure factor has the same peak locations in the spin liquid as in the 120\(^{\circ}\) ordered state, and the phase transitions into the 120\(^{\circ}\) and collinear stripe ordered states are continuous and first-order, respectively.