  We compare the dynamical mean-field descriptions of the single-band Hubbard
model and the three-band Emery model at the one- and two-particle level for
parameters relevant to high-Tc superconductors. We show that even within
dynamical mean-field theory, accounting solely for temporal fluctuations, the
intrinsic multi-orbital nature of the Emery model introduces effective
non-local correlations. These lead to a non-Curie-like temperature-dependence
of the magnetic susceptibility, also seen in nuclear magnetic resonance
experiments in the pseudogap regime by M. Avramovska, et al. [Journal of
Superconductivity and Novel Magnetism 33, 2621 (2020)]. We demonstrate the
agreement of our results with these experiments for a large range of dopings
and trace back the effective non-local correlations to an emerging
oxygen-copper singlet by analyzing a minimal finite-size cluster model. Despite
this correct description of the hallmark of the pseudogap at the two-particle
level, i.e., the drop in the Knight shift of nuclear magnetic resonance,
dynamical mean-field theory fails to properly describe the spectral properties
of the pseudogap.
