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

Abstract

We obtain the complete phase diagram of the antiferromagnetic $J_1$-$J_2$ 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 N\' eel 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 $N\to \infty$ and agree with numerical results from different methods.

4 pages, 5 figures

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Cited by in corpus (5)

• Ground-State Ordering of the $J_1$--$J_2$ Model on the Simple Cubic and Body-Centered Cubic Lattices
• The two-dimensional $t$-$t^{\prime }$ Holstein model
• The Quantum Cluster Variational Method and the Phase Diagram of the quantum ferromagnetic $J_1$-$J_2$ model
• Spin-$1$ $J_1-J_2-J_3$ ferromagnetic Heisenberg model with an easy-plane crystal field on the cubic lattice: A bosonic approach
• Shared purity and concurrence of a mixture of ground and low-lying excited states as indicators of quantum phase transitions