Hartree-Fock Approximation to the Heisenberg Antiferromagnet

The properties of a Heisenberg antiferromagnet at low temperatures are calculated by assuming the two-sublattice structure and by using the double-time Green's-function formalism. The two-particle Green's function is decoupled according to the Hartree-Fock approximation, which differs from the random-phase approximation by an additional term. Since the two-particle Green's function in our problem contains particles of different lattices, the kinematical condition does not enter into this approximation. Numerical results for the ground-state energy and the magnetization are presented.