Spatially Anisotropic Spin J₁-J₂ Heisenberg Model for an Antiferromagnetic Square Lattice: Phase Diagrams

The new magnetic materials such as the layered oxide high-temperature superconductor can be well described by the Heisenberg spin model with nearest-neighbor coupling J₁ and next-nearest-neighbor coupling J₂. A generalization of the J₁-J₂ model is the J₁^{x}-J₁^{y}-J₂ model where the nearest-neighbor bonds have different strengths J₁^{x} and J₁^{y} in the x and y directions, respectively. The effect of the couplings J₂ and J₁^{y} on the antiferromagnetic Néel state is investigated within the quantum many-body Green function method.