Liquid-Liquid Transition in Kitaev Magnets Driven by Spin Fractionalization

While phase transitions between magnetic analogs of three states of matter --- a long-range ordered state, paramagnet, and spin liquid --- have been extensively studied, the possibility of ``liquid-liquid'' transitions, namely, between different spin liquids, remains elusive. By introducing the Ising coupling into the honeycomb Kitaev model with bond asymmetry, we discover that the Kitaev spin liquid becomes a bond-nematic quantum paramagnet before magnetically ordered. The phase transition between the two liquid-like states with different topological nature is of first order, driven by delocalization of the Z$_{\mathrm{2}}$ gauge fluxes, and persists to a critical point at finite temperature located inside the regime where quantum spins are fractionalized. It is suggested that similar transitions may occur in other perturbed Kitaev magnets with bond asymmetry.