# Relevance of Cu-3d multiplet structure in models of high Tc cuprates

## TL;DR

This paper investigates the electronic structure of doped cuprates, emphasizing the importance of Cu-3d multiplet effects and realistic O-2p band modeling, revealing limitations of simplified models like the Zhang-Rice singlet approximation.

## Contribution

It demonstrates that realistic O-2p band structures significantly alter spectral predictions and highlights the role of ligand orbitals and additional low-energy states beyond traditional models.

## Key findings

- Quantitative differences from previous models when using realistic O-2p bands.
- Ligand O-2p orbitals are essential in the impurity model.
- Ground state overlaps only ~50% with Zhang-Rice singlet, indicating other states are important.

## Abstract

We revisit the problem of the spectra of two holes in a CuO$_{2}$ layer, modeled as a Cu-d$^{8}$ impurity with full multiplet structure coupled to a full O-2p band as an approximation to the local electronic structure of a hole doped cuprate. Unlike previous studies that treated the O band as a featureless bath, we describe it with a realistic tight binding model. While our results are in qualitative agreement with previous work, we find considerable quantitative changes when using the proper O-2p band structure. We also find (i) that only the ligand O-2p orbitals play an essential role, within this impurity model; (ii) that the three-orbital Emery model provides an accurate description for the subspace with $^{1}\!A_1$ symmetry, which includes the ground-state in the relevant region of the phase diagram; (iii) that this ground-state has only $\sim 50\%$ overlap with a Zhang-Rice singlet; (iv) that there are other low-energy states, in subspaces with different symmetries, that are absent from the three-orbital Emery model and its one-band descendants. These states play an important role in describing the elementary excitations of doped cuprates.