Chern-Simons theory for magnetization plateaus of the frustrated J₁-J₂ Heisenberg model

The magnetization curve of the two-dimensional spin-1/2 J₁-J₂ Heisenberg model is investigated by using the Chern-Simons theory under mean-field approximations. We find that the magnetization curve increases monotonically for J₂/J₁<0.267949, where the system under zero external field is in the antiferromagnetic Néel phase. For larger ratios of J₂/J₁, various plateaus will appear in the magnetization curve. In particular, in the disordered phase, our results support the existence of the M/M_sat = 1/2 plateau, and predict a plateau at M/M_sat = 1/3. Verification of these interesting results would indicate a strong connection between the frustrated antiferromagnetic system and the quantum Hall system.