Rotational invariance and order-parameter stiffness in frustrated quantum spin systems

We compute, within the Schwinger-boson scheme, the Gaussian-fluctuation corrections to the order-parameter stiffness of two frustrated quantum spin systems: the triangular-lattice Heisenberg antiferromagnet and the $J_1\mathrm{-}{J}_2$ model on the square lattice. For the triangular-lattice Heisenberg antiferromagnet we found that the corrections weaken the stiffness, but the ground state of the system remains ordered in the classical $120°$ spiral pattern. In the case of the $J_1\mathrm{-}{J}_2$ model, with increasing frustration the stiffness is reduced until it vanishes, leaving a small window $0.53\lesssim \eta \lesssim 0.64$ where the system has no long-range magnetic order. In addition, we discuss several methodological questions related to the Schwinger-boson approach. In particular, we show that the consideration of finite clusters which require twisted boundary conditions to fit the infinite-lattice magnetic order avoids the use of ad hoc factors to correct the Schwinger-boson predictions.