We argue that tetragonal CuO (T-CuO) has the potential to finally settle long-standing modelling issues for cuprate physics. We compare the one-hole quasiparticle (qp) dispersion of T-CuO to that of cuprates, in the framework of the strongly-correlated ($U_{dd}rightarrow infty$) limit of the three-band Emery model. Unlike in CuO$_2$, magnetic frustration in T-CuO breaks the $C_4$ rotational symmetry and leads to strong deviations from the Zhang-Rice singlet picture in parts of the reciprocal space. Our results are consistent with angle-resolved photoemission spectroscopy data but in sharp contradiction to those of a one-band model previously suggested for them. These differences identify T-CuO as an ideal material to test a variety of scenarios proposed for explaining cuprate phenomenology.
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