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

Abstract

Using low-energy projection of the one-band $t$-${t}^{\ensuremath{'}}$-${t}^{\ensuremath{'}\ensuremath{'}}$ 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 La${}_{2}$CuO${}_{4}$, Sr${}_{2}$CuO${}_{2}$Cl${}_{2}$, and Bi${}_{2}$Sr${}_{2}$YCu${}_{2}$O${}_{8}$. 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.