Multiple magnon modes in spin- 12 Heisenberg antiferromagnet on simple square lattice in strong magnetic field

We discuss spin-$\frac{1}{2}$ Heisenberg antiferromagnet on simple square lattice in magnetic field $H$ using a recently proposed bond-operator technique. It is well known that magnetically ordered phases of quantum magnets are well described at least qualitatively by the conventional spin-wave theory that only introduces quantum corrections into the classical solution of the problem. We observe that quantum fluctuations change drastically dynamical properties of the considered model at $H$ close to its saturation value: the dynamical structure factor shows anomalies corresponding to Green's function poles which have no counterparts in the spin-wave theory. That is, quantum fluctuations produce multiple short-wavelength magnon modes not changing qualitatively the long-wavelength spin dynamics. Our results are in agreement with previous quantum Monte Carlo simulations and exact diagonalization of finite clusters.