Quantum compass Heisenberg model on the square lattice

The quantum compass model is important for the field of strongly correlated systems with orbital degeneracy and of solid state based devices proposed for quantum computing. I study the compass model with the addition of Heisenberg interactions. I consider a model on the square lattice, with x and z axis. The nearest neighbor interactions are of two types: (a) frustrated interaction Jx and Jz, and (b) Heisenberg interaction along both axis with exchange J.The compass interactions depend on the bond direction. The model is characterized by a high level of frustration. I use a non-linear spin wave theory where four term operators are treated in a self consistent mean field approximation. I calculate all the possible ordered phases at zero temperature, either with ferromagnetic or antiferromagnetic order. I also calculate the spin structure factors and obtain the magnetization as a function of temperature for the Ising-like phases.