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

TL;DR

This paper uses Chern-Simons theory to analyze the magnetization plateaus in the frustrated $J_1$-$J_2$ Heisenberg model, revealing phase boundaries and predicting new plateaus in the magnetization curve.

Contribution

It introduces a mean-field Chern-Simons approach to identify magnetization plateaus and phase boundaries in the $J_1$-$J_2$ Heisenberg model, connecting frustrated magnetism with quantum Hall physics.

Findings

Identification of the 1/2 magnetization plateau in the disordered phase.

Prediction of a new 1/3 magnetization plateau.

Accurate determination of the phase boundary between Néel and disordered phases.

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 N\'eel 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 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.