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

Abstract

The one-band and three-band Hubbard models which describe the electronic structure of cuprates indicate very different values of effective electronic parameters (EPs), such as the Cu on-site Coulomb energy and the Cu-O hybridization strength. In contrast, a comparison of EPs of several cuprates with corresponding values from spectroscopy and scattering experiments indicates similar values in the three-band model and cluster model calculations used to simulate experimental results. To explore this relation in detail, a Cu$_2$O cluster model calculation was carried out to obtain an expression for the Heisenberg exchange coupling $J$ between Cu sites using a downfolding method, taking into account Cu and O on-site correlations ($U_d$ and $U_p$), the charge-transfer energy $\Delta$ and the hopping $t$ between Cu and O sites. A quantitative analysis provides a consistent description of $J$ from neutron scattering experiments, using the three-band model and spectroscopic EPs. In addition, $J$ can be expressed in the one-band Hubbard model form with $\tilde{U}$ and $\tilde{t}$, which denote renormalized $U$ and $t$ using $\Delta$ and $U_p$, and their values indicate a large $\tilde{U}/\tilde{t}$, in agreement with reported values. The large $\tilde{U}/\tilde{t}$ arising from a combination of $U_d$, $U_p$ and $\Delta$ is thus hidden in the effective one-band Hubbard model. The ground-state singlet weights obtained from an exact diagonalization show the importance of the Cu-O Zhang-Rice singlet in the effective one-band Hubbard model. The results provide a consistent method to connect EPs 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.Comment: 9 pages, 2 figures (submitted to Physical Review B