such as the manganites, vanadates, nickelates—or the ruthenates studied here [@Imada1998; @Khomskii2014]. In this case the effective models are far more involved and are never of the single-band $t$–$J$ or Hubbard variety. Can one thus expect that some of the principles of the spin polaron physics do hold there?

To investigate this rather general problem, we take a closer look at one of the intensively investigated transition metal oxides—Ca$_2$RuO$_4$ [@Alexander1999; @Nakatsuji2000; @Mizokawa2001; @Lee2002; @Gorelov2010; @Kunkemoeller2015; @Fatuzzo2015; @Kunkemoeller2017; @Jain2017; @Sutter2017; @Zhang2017; @Das2018; @Ricco2018; @Pincini2019; @Gretarsson2019] which is a spin $S=1$ antiferromagnetically ordered [@Mizokawa2001; @Kunkemoeller2015; @Kunkemoeller2017; @Das2018; @Pincini2019] and Mott insulating analogue of the unconventional superconductor Sr$_2$RuO$_4$ [@Maeno1994]. The other reason for choosing this system is that recently its detailed photoemission spectrum was not only studied experimentally but also successfully modelled using a multiband Hubbard model [@Sutter2017]. Nevertheless, as the multiband Hubbard model was solved using the single-site dynamical mean-field theory approach, it is not clear to what extent the spin polaron physics is present there.

In this paper we concentrate on the origin of the incoherent and almost momentum-independent Ca$_2$RuO$_4$ photoemission spectrum, that is present at the high-binding energy part \[see the yellow rectangle of Fig. \[result\](a)\] and is associated with 