  Using low-energy projection of the one-band t-t'-t"-Hubbard model we derive
an effective spin-Hamiltonian and its spin-wave expansion to order 1/S. We fit
the spin-wave dispersion of several parent compounds to the high-temperature
superconducting cuprates: La2CuO4, Sr2CuO2Cl2 and Bi2Sr2YCu2O8. Our accurate
quantitative determination of the one-band Hubbard model parameters allows
prediction and comparison to experimental results of measurable quantities such
as staggered moment, double occupancy density, spin-wave velocity and bimagnon
excitation spectrum and density of states, which is discussed in relation to
K-edge RIXS and Raman experiments.
