Ordered moment in the anisotropic and frustrated square lattice Heisenberg model

Abstract

The two-dimensional frustrated next-to-nearest-neighbor Heisenberg model on the square lattice is a prime example for a spin system where quantum fluctuations can either destroy or stabilize magnetic order. The phase boundaries and staggered moment dependence on the frustration ratio ${J}_{2}/{J}_{1}$ of the exchange constants are fairly well understood both from approximate analytical and numerical methods. In this work we use exact diagonalization for finite clusters for an extensive investigation of the more general ${J}_{1a,b}$-${J}_{2}$ model which includes a spatial exchange anisotropy between next-neighbor spins. We introduce a systematic way of tiling the square lattice and, for this low symmetry model, define a controlled procedure for the finite size scaling that is compatible with the possible magnetic phases. We obtain ground-state energies, structure factors, and ordered moments and compare with the results of spin-wave calculations. We conclude that ${J}_{1a,b}$ exchange anisotropy strongly stabilizes the columnar antiferromagnetic phase for all frustration parameters, in particular in the region of the spin nematic phase of the isotropic model.