Spin dynamics and antiferromagnetic short-range order in the two-dimensional Heisenberg model

We investigate the spin dynamics in the presence of short-range order in the square lattice $S=\frac{1}{2}$ Heisenberg antiferromagnet by a spin-rotation-invariant Green’s-function theory for the dynamic spin susceptibility. The self-energy is calculated in the lowest-order Born approximation using the results of a sum-rule–conserving mean-field approximation. In the spin-wave region, where the damping of magnons is found to be small compared with their energy, the dynamic structure factor is obtained in reasonable agreement with Monte Carlo data. Moreover, the structure factor yields an indication of the crossover to the relaxation region.