Spectral characteristics of the antiferromagnetic spin-1/2 Heisenberg model on the square lattice in a magnetic field

We predict that spin-waves in an ordered square quantum antiferromagnet in a magnetic field (h) perpendicular to antiferromagnetic plane may demonstrate three modes of spin excitations. Starting from the self-consistent rotation-invariant Green's function method, a new mean-field theory is constructed for h not equal 0. The method preserves the translational and the axial symmetries, and provides exact fulfillment of the single-site constraint for each of the three modes. We examine the dynamical structure factors S-alpha alpha(k, omega),alpha(beta) = x, y, z. It is shown, that the introduction of h leads to the hybridization of two degenerate spin modes due to the appearance of a non-diagonal on alpha, beta spin-spin Green's functions. The comparison of the theory with the exact diagonalization study and with results on inelastic neutron scattering experiments is discussed at T = 0. We discuss also the correspondence of the present theory to the existing theories, which allow only two spin excitations modes for the total S(k, omega).