Spin-spin correlation functions for the square-lattice Heisenberg antiferromagnet at zero temperature

We have calculated the dynamical transverse and longitudinal spin-correlation functions for the two-dimensional Heisenberg antiferromagnet at zero temperature, by the Dyson-Maleev spin-wave theory to second order in perturbation theory. The transverse correlation function is characterized by a dominant one-magnon peak and a broad three-magnon continuum. For spin 1/2 the contribution of the three-magnon excitations is small but not negligible, and might be detected in highly sensitive neutron-scattering experiments in the undoped layered cuprates. We have also computed the transverse equal-time correlations and compared the results with recent series-expansion estimates. The good agreement between the two formalisms reinforces the validity of spin-wave theory. The longitudinal structure factor, to leading order, displays a two-peak structure similar to that obtained by the Schwinger-boson mean-field formalism. The magnon interaction reduces the second peak, in some cases substantially. We discuss how umklapp processes affect the multiple-magnon excitations. We have finally computed the staggered magnetization and transverse susceptibility corrected to second order. For spin 1/2 we find m=0.3069±0.00020 for the staggered magnetization, and ${\mathit{Z}}_{\mathrm{\chi }}$=0.4844±0.00010 for the susceptibility renormalization constant, in agreement with the results obtained by other techniques.