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

TL;DR

This paper demonstrates a method to connect the one-band and three-band Hubbard models of cuprates by aligning electronic parameters with experimental data, revealing their underlying equivalence.

Contribution

It introduces a way to relate one-band and three-band models using experimental spectroscopy and scattering data, clarifying their equivalence in describing cuprates.

Findings

Effective parameters from spectroscopy match three-band model calculations.

The Heisenberg exchange $J$ aligns with neutron scattering results.

The models are shown to be fundamentally equivalent through parameter mapping.

Abstract

The one-band 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 model 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 $\tilde{U}$ and $\tilde{t}$ are described using the three band parameters, thus revealing the hidden equivalence of the one-band 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.