Chern-Simons Theory for Magnetization Plateaus of Frustrated $J_1$-$J_2$ Heisenberg model

The magnetization curve of the two-dimensional spin-1/2 $J_1$-$J_2$ Heisenberg model is investigated by using the Chern-Simons theory under a uniform mean-field approximation. We find that the magnetization curve is monotonically increasing for $J_2\mathrm{/}{J}_1<0.267949$, where the system under zero external field is in the antiferromagnetic N'eel phase. For larger ratios of $J_2\mathrm{/}{J}_1$, various plateaus will appear in the magnetization curve. In particular, in the disordered phase, our result supports the existence of the $M\mathrm{/}{M}_{\mathrm{s}\mathrm{a}\mathrm{t}}=1\mathrm{/}2$ plateau and predicts a new plateau at $M\mathrm{/}{M}_{\mathrm{s}\mathrm{a}\mathrm{t}}=1\mathrm{/}3$. By identifying the onset ratio $J_2\mathrm{/}{J}_1$ for the appearance of the 1/2-plateau with the boundary between the N'eel and the spin-disordered phases in zero field, we can determine this phase boundary accurately by this mean-field calculation. Verification of these interesting results would indicate a strong connection between the frustrated antiferromagnetic system and the quantum Hall system.