Universal thermodynamics in the Kitaev fractional liquid

In the Kitaev honeycomb model, the quantum spin fractionalizes into itinerant Majorana fermion and gauge flux upon cooling, leading to rich experimental ramifications at finite temperature and an upsurge of research interest. However, accurate modelings of the Kitaev materials by including realistic couplings beyond the pure Kitaev model constitute a major challenge for the community. With recently developed exponential tensor-network approach, we clear the pathway and perform finite-temperature simulations of the extended Kitaev model with additional interactions common in real materials. At intermediate temperature, we find an emergent Curie law of magnetic susceptibility and a stripy spin-structure factor characterizing the robust Kitaev fractional liquid. With this insight, we revisit the susceptibility measurements of Na₂IrO₃ and α -RuCl₃ and find evidence of ferromagnetic Kitaev coupling and finite-temperature fractionalization. Bridging the gap between theories and experiments with the state-of-the-art tensor-network simulations, our findings provide guidance for future experimental exploration of the spin liquids in Kitaev materials by thermodynamic measurements and spin-resolved structure factor probes.