J 2 quantum Heisenberg antiferromagnet : Improved spin - wave theories versus exact - diagonalization data

We reconsider the results cocerning the extreme-quantum S = 1/2 square-lattice Heisenberg antiferromagnet with frustrating diagonal couplings (J 1 − J 2 model) drawn from a comparison with exact-diagonalization data. A combined approach using also some intrinsic features of the self-consistent spin-wave theory leads to the conclusion that the theory strongly overestimates the stabilizing role of quantum flutcuations in respect to the Néel phase in the extreme-quantum case S = 1/2. On the other hand, the analysis implies that the Néel phase remains stable at least up to the limit J 2 /J 1 = 0.49 which is pretty larger than some previous estimates. In addition, it is argued that the spin-wave ansatz predicts the existence of a finite range (J 2 /J 1 < 0.323 in the linear spin-wave theory) where the Marshall-Peierls sigh rule survives the frustrations.