contain several degrees of freedom. On the other, this is due to the fact that such relatively simple models are often not solvable in the thermodynamic limit. That is why examples when a theoretical model can be solved without too drastic approximations [*and*]{} explain the experimentally observed features of a correlated oxide are of interest. One such case, known already since the end of the 80s of the last century, is the so-called spin polaron problem [@Schmitt1988; @Martinez1991; @Ramsak1998; @Manousakis2007; @Wang2015; @Grusdt2018; @Bieniasz2019], which explains the peak dispersion found in the photoemission spectrum of the (spin $S=1/2$) antiferromagnetically ordered and Mott insulating copper oxides [@Wells1995; @LaRosa1997; @Kim1998; @Damascelli2003; @Shen2007]: It turns out that the peak dispersion found in the spectra of the ‘parent compounds’ to the high-temperature superconductors can be well explained using a $t$–$J$ or Hubbard model that is mapped onto a (spin) polaron problem.

Interestingly, despite the still unresolved mysteries associated with high-temperature superconductivity, the copper oxides are the simplest class of oxides to model. This is basically due to the fact that the uncorrelated part of their physics can be effectively described using a single-band picture [@Zhang1988; @Lee2006]. Such situation is not realised in many other oxides, 