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Using the exact diagonalization technique, we determine the energy spectrumand wave functions for finite chains described by the two-spin(Kugel--Khomskii) model with different types of intersubsystem exchange terms.The found solutions provide a possibility to address the problem of quantumentanglement inherent to this class of models. We put the main emphasis on thecalculations of the concurrence treated as an adequate numerical measure of theentanglement. We also analyze the behavior of two-site correlation functionsconsidered as a local indicator of entanglement. We construct the phasediagrams of the models involving the regions of nonzero entanglement. Thepronounced effect of external fields, conjugated to both spin variables on theregions with entanglement, could both enhance and weaken the entanglementdepending on the parameters of the models.

Quantum entanglement, local indicators and effect of external fields in the Kugel-Khomskii model