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 Ј model, in which the nearest-neighbor coupling takes a different value J 1 Ј 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 Ј/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 Ј 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. ͓S0163-1829͑99͒03437-2͔

We compute the Gaussian-fluctuation corrections to the saddle-point Schwinger-boson results using collective coordinate methods. Concrete application to investigate the frustrated J1 −J2 antiferromagnet on the square lattice shows that, unlike the saddle-point predictions, there is a quantum nonmagnetic phase for 0.53 < ∼ J2/J1 < ∼ 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 to Bose condensation. The very good agreement of our results with exact numerical values on finite clusters lends support to the calculational scheme employed.In the last years there has been a lot of interest in the properties of quantum magnetic systems, [1] particularly frustrated quantum antiferromagnets. Although this interest was initially related to the possible connections between magnetism and superconductivity in the ceramic compounds, the current activity in the area is now well beyond this original motivation.Among the analytical methods used to study quantum spin systems, the Schwinger-boson approach [2] is one of the most elegant and successful techniques. Contrary to standard spin-wave theory, it does not rely on having a magnetized ground-state, which leads to nice rotational properties of the results and to the possibility of describing ordered and disordered phases in an unified treatment. However, this theory has the drawback of being defined in a constrained bosonic space, with unphysical configurations being allowed when this constraint is treated as a soft (average) restriction. This drawback can be in principle corrected by including local fluctuations of the boson chemical potential. [3] Despite the widespread use in the literature of the Schwinger-boson representation of quantum spin operators, we are not aware of a complete calculation of Gaussian corrections to saddle-point results. In particular, for frustrated quantum antiferromagnets such calculations have been sketched several times, [2,4,5] but never fully undertaken. In this work we fill up this gap by presenting the general calculation of Gaussian fluctuations in the Schwinger-boson approach. Since the theory presents a local U (1) symmetry, we use collective coordinate methods -as developed in the context of relativistic lattice gauge theories [6]-to handle the infinitely-many zero modes associated to the local symmetry breaking in the saddle-point expansion. As a concrete application, we study the existence and location of the nonmagnetic quantum phase predicted to occur as a consequence of quantum fluctuations and frustration in the J 1 −J 2 model. [7] We will consider a general Heisenberg Hamiltonian,where ij are links on a lattice. We write spin operators in terms of Schwinger bosons:is a bosonic spinor, σ is the vector of Pauli matrices, and there is a bosonnumber restriction σ a † iσ a iσ = 2S on each site. With this faithful representation of the spin algebra, the rotational invariant...