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The effects of quantum fluctuations due to directional anisotropy andfrustration between nearest neighbors and next-nearest neighbors of the quantumspin-1/2 Heisenberg antiferromagnet on a square lattice are investigated usingspin-wave expansion. We have calculated the spin-wave energy dispersion in theentire Brillouin zone, renormalized spin-wave velocities, and the magnetizationup to second order in 1/S expansion for the antiferromagnetic Neel andcollinear antiferromagnetic stripe phases. It is shown that the second-ordercorrections become significant with increase in frustration. With thesecorrections magnetizations and spin-wave velocities for both the phases becomezero at the quantum critical points as expected from other numerical andanalytical methods. We have shown that the transition between the two orderedphases are always separated by the disordered paramagnetic phase.

Second-order quantum corrections for the frustrated, spatially anisotropic, spin-1/2 Heisenberg antiferromagnet on a square lattice