Quantum effects and broken symmetries in frustrated antiferromagnets

We investigate the interplay between frustration and zero-point quantum fluctuations in the ground state of the triangular and J(1)-J(2) Heisenberg antiferromagnets, using finite-size spin-wave theory, exact diagonalization, and quantum Monte Carlo methods. In the triangular Heisenberg antiferromagnet, by performing a systematic size-scaling analysis, we have obtained strong evidences for a gapless spectrum and a finite value of the thermodynamic order parameter, thus confirming the existence of long-range Neel order. The good agreement between the finite-size spin-wave results and the exact and quantum Monte Carlo data also supports the reliability of the spin-wave expansion to describe both the ground state and the low-energy spin excitations of the triangular Heisenberg antiferromagnet. In the J(1)-J(2) Heisenberg model, our results indicate the opening of a finite gap in the thermodynamic excitation spectrum at J(2)/J(1) similar or equal to 0.4, marking the melting of the antiferromagnetic Neel order and the onset of a non-magnetic ground state. In order to characterize the nature of the latter quantum-disordered phase we have computed the susceptibilities for the most important crystal symmetry breaking operators. In the ordered phase the effectiveness of the spin-wave theory in reproducing the low-energy excitation spectrum suggests that the uniform spin susceptibility of the model is very close to the linear spin-wave prediction.