NonlinearσModel Method for theJ1−J2Heisenberg Model: Disordered Ground State with Plaquette Symmetry

A novel nonlinear $\sigma$ model method is proposed for the two-dimensional $J_1\mathrm{\text{−}}{J}_2$ model, which is extended to include plaquette-type distortion. The nonlinear $\sigma$ model is properly derived without spoiling the original spin degrees of freedom. The method shows that a single disordered phase continuously extends from a frustrated uniform regime to an unfrustrated distorted regime. By the continuity and Oshikawa’s commensurability condition, the disordered ground states for the uniform $J_1\mathrm{\text{−}}{J}_2$ model are plaquette states with fourfold degeneracy.