Magnetic and quantum disordered phases in triangular-lattice Heisenberg antiferromagnets

We study, within the Schwinger-boson approach, the ground-state structure of two Heisenberg antiferromagnets on the triangular lattice: the $J_1-J_2$ model, which includes a next-nearest-neighbor coupling $J_2,$ and the spatially-anisotropic $J_1-J_1^{\prime }$ model, in which the nearest-neighbor coupling takes a different value $J_1^{\prime }$ along one of the bond directions. The motivations for the study of these systems range from general theoretical questions concerning frustrated quantum spin models to the concrete description of the insulating phase of some layered molecular crystals. For both models, the inclusion of one-loop corrections to saddle-point results leads to the prediction of nonmagnetic phases for particular values of the parameters $J_1{/J}_2$ and $J_1^{\prime }{/J}_1.$ In the case of the $J_1-J_2$ model we shed light on the existence of such disordered quantum state, a question which is controversial in the literature. For the $J_1-J_1^{\prime }$ model our results for the ground-state energy, quantum renormalization of the pitch in the spiral phase, and the location of the nonmagnetic phases, nicely agree with series expansions predictions.