Connecting the one-band and three-band Hubbard models of cuprates via spectroscopy and scattering experiments

Abstract

The one- and three-band Hubbard models which describe the electronic structure of cuprates indicate very different values of effective electronic parameters, such as the on-site Coulomb energy and the hybridization strength. In contrast, a comparison of electronic parameters of several cuprates with corresponding values from spectroscopy and scattering experiments indicates similar values in the three-band and cluster model calculations used to simulate experimental results. The Heisenberg exchange coupling $J$ obtained by a downfolding method in terms of the three-band parameters is used to carry out an optimization analysis consistent with $J$ from neutron scattering experiments for a series of cuprates. In addition, the effective one-band parameters $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{U}$ and $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{t}$ are described using the three-band parameters, thus revealing the hidden equivalence of the one- and three-band models. The ground-state singlet weights obtained from an exact diagonalization elucidates the role of Zhang-Rice singlets in the equivalence. The results provide a consistent method to connect electronic parameters obtained from spectroscopy and the three-band model with values of $J$ obtained from scattering experiments, band dispersion measurements, and the effective one-band Hubbard model.