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EN
On the example of monolayer manganites we show that the theoretical ideas developed long ago along the derivation of the spin t-J model from the Hubbard model are nowadays very helpful in strongly correlated oxides with partly filled degenerate orbitals. We analyze a realistic orbital t-J model for e_g electrons in La_{1-x}Sr_{1+x}MnO_4 monolayer manganites, and discuss the evolution of spin and orbital correlations under increasing doping by performing exact diagonalization of finite clusters, with electronic kinetic energy determined self-consistently at a finite temperature by classical Monte Carlo for t_{2g} spins. Several experimental results are reproduced.
EN
Using the self-consistent Born approximation we calculate Reiter's wave function for a single hole introduced into the undoped and orbitally ordered ground state of the t-J model with t_{2g} orbital degrees of freedom. While the number of excitations is similar to the spin t-J model for a given J/t, a distinct structure of the calculated wave function and its momentum dependence is identified suggesting the formation of a novel type of mobile polarons.
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Hole Propagation in the Orbital Compass Models

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EN
We explore the propagation of a single hole in the generalized quantum compass model which interpolates between fully isotropic antiferromagnetic phase in the Ising model and nematic order of decoupled antiferromagnetic chains for frustrated compass interactions. We observe coherent hole motion due to either interorbital hopping or due to the three-site effective hopping, while quantum spin fluctuations in the ordered background do not play any role.
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