Exact diagonalization study of the antiferromagnetic spin- 1/2 Heisenberg model on the square lattice in a magnetic field

We study the field dependence of the antiferromagnetic spin-1/2 Heisenberg model on the square lattice by means of exact diagonalizations. In the first part, we calculate the spin-wave velocity c, the spin stiffness ρ_s, and the magnetic susceptibility χ_⊥, and thus determine the microscopic parameters of the low-energy long-wavelength description. In the second part, we present a comprehensive study of dynamical spin-correlation functions for magnetic fields ranging from zero up to saturation. We find that, at low fields, magnons are well defined in the whole Brillouin zone but the dispersion is substantially modified by quantum fluctuations compared to the classical spectrum. At higher fields, decay channels open and magnons become unstable with respect to multimagnon scattering. Our results directly apply to inelastic neutron-scattering experiments.