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In this short review, which is based on the works published between 2011 and2016, we discuss the problem of the propagation of a collective orbitalexcitation (orbiton) created in the Mott insulating and antiferromagneticground state. On the theoretical side, the problem is solved by mapping aKugel-Khomskii spin-orbital model describing an orbiton moving in anantiferromagnet onto an effective t-J model with a 'single hole' moving in anantiferromagnet. The most important consequence of the existence of the abovemapping is the fractionalisation of the electron's spin and orbital degree offreedom in the 1D antiferromagnets---a spin-orbital separation phenomenon thatis similar to the spin-charge separation in 1D but corresponds to an exoticregime where spinons are faster than holons. Besides a detailed explanation andbenchmarking of the mapping, in this review we also discuss its application toseveral relatively realistic spin-orbital models, that are able to describe theexperimentally observed orbital excitation spectra of copper and iridiumoxides.

Propagation of an orbiton in the antiferromagnets: theory and experimental verification