Spectrum and correlation functions of an anisotropic heisenberg antiferromagnet. IV. Model of easy plane type with allowance for Dzyaloshinskii interaction

A study is made of the matrix Green's function that is constructed from Pauli operators and describes the transverse component of the dynamic susceptibility tensor of a twosublattice Heisenberg antiferromagnet of the easy plane type with allowance for the Dzyaloshinskii interaction with spin $1/2$ in longitudinal and transverse magnetic fields. In the generalized Hartree–Fock approximation (without allowance for damping) an expression is found for the renormalized magnon spectrum as well as the equation for the magnetization in all admissible phase states; the phase boundary on the ($H,\Theta$) plane is calculated. It is shown that to satisfy the symmetry requirement and the Bogolyubov–Goldstone theorem in the case of a transverse field in the region of low temperatures it is necessary to take into account the contribution of the mass operator to a higher approximation corresponding to three-magnon scattering processes.