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Thermalisation is a probabilistic process. As such, it is generally expectedthat when we increase the temperature of a system its classical behaviourdominates its quantum coherences. By employing the Gibbs state of atranslationally invariant quantum spin liquid - Kitaev's honeycomb latticemodel - we demonstrate that an insulating phase at $T=0$ becomes metallicpurely by increasing temperature. In particular, we compute the finitetemperature distribution of energies and show that it diverges logarithmically,as we move to small energies. The corresponding wave functions become criticalalike as at Anderson transitions. These characteristics are obtained within anew exact Monte Carlo method that simulates the finite temperature behaviour ofthe Kitaev model. In particular, we take into account the projection onto thephysical parity sectors, required for identifying the topological degeneracy ofthe model. Our work opens the possibility to detect thermal metal behaviour inspin liquid experiments.

Thermally induced metallic phase in a gapped quantum spin liquid - a Monte Carlo study of the Kitaev model with parity projection