Quantum spin fluctuations in an itinerant antiferromagnet

Starting with the Hubbard-model description of an itinerant antiferromagnet, we develop a matrix formulation in the sublattice basis and explicitly obtain the spin-wave propagator. We show that in the strong-coupling limit we not only obtain the same spin-wave mode (Ω_Q=2J √1-γ_Q² ) as for the spin-1/2 Heisenberg model, but by incorporating the quantum, zero-point spin fluctuations represented by spin waves, we also obtain exactly the same sublattice magnetization (0.6 in two dimensions) and ground-state energy [-NJ(1+0.158)] as obtained within the linear spin-wave analysis of the spin-1/2 Heisenberg model. We examine the effect of spin-wave interaction on quasiparticle energies and find that the lowest-energy state for an added hole (or electron) is the k=(±π/2,±π/2) state. We also obtain the spin-wave mode in a highly anisotropic three-dimensional (3D) antiferromagnet and evaluate the zero-point reduction in sublattice magnetization as a function of the interlayer hopping strength.