Particle-particle response function as a probe for electronic correlations in the p-d Hubbard model

We discuss and compare different approximations to the particle-particle response function in the p-d (three-band) Hubbard model for the CuO2 plane of superconducting cuprates. Besides the relevance for understanding the role of correlations in high-Tc superconductors, the interest in the CuO2 plane is due to the presence of three incompletely filled valence bands. The bare ladder approximation (BLA) was employed long ago in the context of Auger core-valence-valence spectroscopy of late transition metals while the time-dependent (TD) Gutzwiller approximation (GA) is a much more sophisticated and recent development. The validity of both is assessed by comparing with exact-diagonalization results from a finite six-site cluster. We find that for standard parameter sets TDGA and BLA yield two-hole spectra in excellent agreement with the exact ones. Although the interaction is comparable to the kinetic energy, the system is far from the extreme Mott limit often assumed in cuprates, where the Mott insulating character is completely local. In order to identify possible fingerprints of the extreme Mott regime we artificially reduce the bandwidth. We find that the BLA breaks down while the TDGA keeps near the exact results. Our findings provide a simple criterion to identify doped and undoped extreme Mott insulators.