In this paper, the topology of world lines is connected to basic statistic rules of elementary particles, and the possibility of anyons with intriguing statistical properties in two-dimensional worlds is discussed. Quantum spin liquids, characterized by an absence of local order parameter and fractionalized spin degrees of freedom, are presented as a candidate, where quasiparticle excitations in the form of anyons could occur. The exactly solvable Kitaev spin model on a honeycomb lattice, which predicts an emergence of a spin liquid ground state, is analysed in detail. Firstly, the physical background of frustrated bond-directional interactions is explored and the spin degrees of freedom are rewritten using Majorana fermions. The fractionalization of spins into static gauge fluxes and mobile Majorana fermions, forming two types of excitations, can be exploited as a signature of a spin liquid behaviour in experimental realizations of the Kitaev model. Lastly, measurements of specific heat and dependence of the spin excitation gap on the external magnetic field in the Kitaev material ?-RuCl3 are shown as experimental results that support theoretical predictions of spin fractionalization.

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