Schwinger-Boson Approach to Quantum Spin Systems: Gaussian Fluctuations in the “Natural” Gauge

We compute the Gaussian-fluctuation corrections to the saddle-point Schwinger-boson results using collective coordinate methods. Concrete application to investigate the frustrated $J_1-J_2$ antiferromagnet on the square lattice shows that, unlike the saddle-point predictions, there is a quantum nonmagnetic phase for $0.53\lesssim J_2{/J}_1\lesssim 0.64$. This result is obtained by considering the corrections to the spin stiffness on large lattices and extrapolating to the thermodynamic limit, which avoids the infinite-lattice infrared divergencies associated with Bose condensation. The very good agreement of our results with exact numerical values on finite clusters lends support to the calculational scheme employed.