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

Ming-Che Chang·Min-Fong Yang
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Abstract

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 $J_2/J_1 < 0.267949$, where the system under zero external field is in the antiferromagnetic Néel phase. For larger ratios of $J_2/J_1$, various plateaus will appear in the magnetization curve. In particular, in the disordered phase, our result supports the existence of the $M/M_{\rm sat}=1/2$ plateau and predicts a new plateau at $M/M_{\rm sat}=1/3$. By identifying the onset ratio $J_2/J_1$ for the appearance of the 1/2-plateau with the boundary between the Néel 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.

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Ming-Che Chang, Min-Fong Yang. 2002-04-25. Chern-Simons Theory for Magnetization Plateaus of Frustrated $J_1$-$J_2$ Heisenberg model. https://doi.org/10.1103/physrevb.66.184416

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