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While phase transitions between magnetic analogs of three states of matter--- a long-range ordered state, paramagnet, and spin liquid --- have beenextensively studied, the possibility of "liquid-liquid" transitions, namely,between different spin liquids, remains elusive. By introducing the additionalIsing coupling into the honeycomb Kitaev model with bond asymmetry, we discoverthat the Kitaev spin liquid turns into a spin-nematic quantum paramagnet beforea magnetic order is established by the Ising coupling. The quantum phasetransition between the two liquid states accompanies a topological changedriven by fractionalized excitations, the $Z_2$ gauge fluxes, and is of firstorder. At finite temperatures, this yields a persisting first-order transitionline that terminates at a critical point located deep inside the regime wherequantum spins are fractionalized. It is suggested that similar transitions mayoccur in other perturbed Kitaev magnets with bond asymmetry.

Spin-Liquid--to--Spin-Liquid Transition in Kitaev Magnets Driven by Fractionalization