  We investigate the tetragonal phase of the binary transition metal oxide CuO
(t-CuO) within the context of cellular dynamical mean-field theory. Due to its
strong antiferromagnetic correlations and simple structure, analysing the
physics of t-CuO is of high interest as it may pave the way towards a more
complete understanding of high temperature superconductivity in hole-doped
antiferromagnets. In this work we give a formal justification for the weak
coupling assumption that has previously been made for the interconnected
sublattices within a single layer of t-CuO by studying the non-local
self-energies of the system. We compute momentum-resolved spectral functions
using a Matrix Product State (MPS)-based impurity solver directly on the real
axis, which does not require any numerically ill-conditioned analytic
continuation. The agreement with photoemission spectroscopy indicates that a
single band Hubbard model is sufficient to capture the material's low energy
physics. We perform calculations on a range of different temperatures, finding
two magnetic regimes, for which we identify the driving mechanism behind their
respective insulating state. Finally, we show that in the hole-doped regime the
sublattice structure of t-CuO has interesting consequences on the symmetry of
the superconducting state.
