Two-dimensional Heisenberg antiferromagnet with next-nearest-neighbor coupling

We study the two-dimensional $S=\frac{1}{2}$ antiferromagnet with next-nearest-neighbor antiferromagnetic coupling using a sublattice-symmetric spin-wave theory and exact diagonalization. For sufficiently large frustration the theory predicts a transition to a disordered state with an energy gap and exponentially decaying correlations, rather than to a gapless spin-liquid state. Comparison with exact results on finite lattices up to 26 sites indicates that the theory overestimates the disordering effect of the next-nearest-neighbor coupling, implying that the long-range antiferromagnetic order is surprisingly robust.