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arXiv · 1504.01334

Magnetic quantum phase transitions of the antiferromagnetic J_{1}-J_{2} Heisenberg model

T. P. Cysne·M. B. Silva Neto
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Abstract

We obtain the complete phase diagram of the antiferromagnetic $J_{1}$-$J_{2}$ model, $0\leq \alpha = J_2/J1 \leq 1$, within the framework of the $O(N)$ nonlinear sigma model. We find two magnetically ordered phases, one with N\' eel order, for $\alpha \leq 0.4$, and another with collinear order, for $\alpha\geq 0.6$, separated by a nonmagnetic region, for $0.4\leq \alpha \leq 0.6$, 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 $N\rightarrow\infty$ and agree with numerical results from different methods.

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T. P. Cysne, M. B. Silva Neto. 2015-04-06. Magnetic quantum phase transitions of the antiferromagnetic J_{1}-J_{2} Heisenberg model. https://doi.org/10.1209/0295-5075/112/47002

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