a spectrum \[Fig. \[result\](c)\] which surprisingly well resembles the high binding energy part of the observed experimental spectrum \[Fig. \[result\](a)\]: both spectra have an incoherent character, without a clear quasiparticle band emerging, and only very weak dependence of its intensity on the momentum. (A weak dependence on the momentum of the intensities in the high binding energy part of the observed experimental spectrum \[Fig. \[result\](a)\] originates in the $xy$ orbital spectral function, not considered here but explained in detail in Ref. .) What is more, the low- and high-energy edges of both broad spectra are basically momentum-independent. Finally, also the overall energy scale, which is given by the width of the broad spectrum estimated at the half maximum intensity, is of the same order of magnitude in both cases and amounts to about $0.5$ eV.

Discussion. {#sec:discussion}
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What might be the origin of the onset of such an incoherent, almost momentum-independent and, apart from the horizontal ‘stripes’, rather featureless spectrum of Fig. \[result\](b)? Looking first at model (\[model1\]-\[model2\]) we can immediately note what distinguishes it from the ‘standard’ $S=1/2$ $t$–$J$ model, that has been widely used to describe the photoemission spectra of the undoped cuprates [@Schmitt1988; @Martinez1991; @Ramsak1998; @Manousakis2007; 