Unified one-band Hubbard model for magnetic and electronic spectra of the parent compounds of cuprate superconductors

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. Among those we discuss the two-magnon Raman peak line shape, the K-edge resonant inelastic x-ray scattering 500-meV peak, and the high-energy kink in the angle-resolved photoemission spectroscopy quasiparticle dispersion, also known as the waterfall feature.