but no spin anisotropy, i.e. model (\[model1\]-\[model2\]) with ${\bf e}_{xz} = \hat{x}$ and ${\bf e}_{yz}=\hat{y}$; and (d) the spin $S=1$ $t$–$J$ model with both anisotropies present as suggested for Ca$_2$RuO$_4$ and equivalent to Fig. \[result\](b), i.e. model (\[model1\]-\[model2\]) with ${\bf e}_{xz} = \hat{x}$, ${\bf e}_{yz}=\hat{y}$, and all model parameters as in Fig. \[result\](b). All spectra normalised as Fig. \[result\]. []{data-label="fourplots"}](fig2.png){width="50.00000%"}

We explore the above-listed differences in detail by comparing the spectral function $A({\bf k}, \omega)$ calculated for the distinct versions of the relevant $t$–$J$ models, cf. Fig. \[fourplots\]. Firstly, it is evident that the effects of the spin anisotropy are profound, see Figs. \[fourplots\] (c) and (d). On the one hand, it makes the spectrum less dispersive and in general more featureless; on the other it leads to the formation of a horizontal stripes superimposed onto the otherwise featureless spectrum. Both the former and the latter can be understood, when one considers the fact that the very large anisotropy limit leads, in this case, to the dominant Ising-like interactions between spins. This triggers the hole confinement in a linear string potential and leads to a well-known ladder-like spectrum with the horizontal ‘stripes’ [@Martinez1991; @Dagotto1994; @Bieniasz2018].

![The one dimensional character of 