Magnetic quantum phase transitions of the two-dimensional antiferromagnetic J₁-J₂ Heisenberg model

We obtain the complete magnetic phase diagram of the two-dimensional antiferromagnetic $J_1\text{-}{J}_2$ Heisenberg model, $0\le \alpha =J_2/J1\le 1$, within the framework of the O(N) nonlinear sigma model. We find two magnetically ordered phases, one with Néel order, for $\alpha \le 0.4$, and another with collinear order, for $\alpha \ge 0.6$, separated by a nonmagnetic region, for $0.4\le \alpha \le 0.6$, where a gapped spin liquid is found. The transition at $\alpha =0.4$ is of the second order while the one at $\alpha =0.6$ is of the first order and the spin gaps cross at $\alpha =0.5$. Our results are exact at N → ∞ and agree with numerical results from different methods. (letter)