Magnetic Properties of Quantum Square Heisenberg Antiferromagnet with Frustration: an Auxiliary Fermion Approach

We study the magnetic ordered phases of the spin \(-\frac{1}{2}\) Heisenberg antiferromagnetic model with nearest \(J_1\) and next nearest neighbor \(J_2\) exchange interactions on the square lattice using fermionic representation of spin operators within Popov-Fedotov approach.The unphysical states are eliminated on each site by introducing an imaginary chemical potential. Working in local coordinate system for every site we investigate the different ordered phases in dependence on exchange parameters. At \(T = 0\) we recover the conventional spin wave results.