Spectrum and correlation functions of an anisotropic Heisenberg antiferromagnet I. Antiferromagnetic phase in the generalized Hartree-Fock approximation

A study is made of a matrix Green's function constructed with Pauli operators and describing the transverse components of the dynamic susceptibility tensor Of a two-sublattice anisotropic Heisenberg antiferromagnet with spin 1/2 in a longitudinal magnetic field. In the generalized Hartree–Fook approximation (without allowance for damping) the renormalized magnon spectrum and the one-particle (normal and anomalous) correlation functions in the antiferromagnetic phase are found. The cases of easy-plane and easy-axis anisotropy are studied in detail; in the second case the phase boundary at low temperatures and near the N6el point is calculated.