Square-lattice Heisenberg antiferromagnet with two kinds of nearest-neighbor regular bonds

We study the zero-temperature phase diagram of a square-lattice S=1/2 Heisenberg antiferromagnet with two types of regularly distributed nearest-neighbor exchange constants, ${\mathit{J}}_1$≳0 (antiferromagnetic) and -∞<${\mathit{J}}_2$<∞, using spin-wave series based on appropriate mean-field Hamiltonian and exact-diagonalization data for small clusters. At a semiclassical level, the model displays two critical points separating the Néel state from (i) a helicoidal magnetic phase for relatively small frustrating ferromagnetic couplings ${\mathit{J}}_2$<0 (${\mathit{J}}_2$/${\mathit{J}}_1$<-1/3 for classical spins), and (ii) a finite-gap quantum paramagnetic phase for large enough antiferromagnetic exchange constants ${\mathit{J}}_2$≳0. The quantum order-disorder transition (ii) is similar to the one recently studied in two-layer Heisenberg antiferromagnets and is a pure result of the zero-point spin fluctuations. On the other hand, the melting of the Néel state in the ferromagnetic region, ${\mathit{J}}_2$<0, is a combined effect of the frustration and quantum spin fluctuations. The second-order spin-wave calculations of the ground-state energy and on-site magnetization are in accord with our exact-diagonalization data in a range away from the quantum paramagnetic phase. In approaching the phase boundary, the theory fails due to the enhanced longitudinal-spin fluctuations, as it has recently been argued by Chubukov and Morr.