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

Thermalization is a probabilistic process. As such, it is generally expected that when we increase the temperature of a system, its classical behavior dominates its quantum coherences. By employing the Gibbs state of a translationally invariant quantum spin liquid—Kitaev's honeycomb lattice model—we demonstrate that an insulating phase at T=0 becomes metallic purely by increasing temperature. In particular, we compute the finite-temperature distribution of energies and show that it diverges logarithmically, as we move to small energies. The corresponding wave functions become critical like at Anderson transitions. These characteristics are obtained within an exact Monte Carlo method that simulates the finite-temperature behavior of the Kitaev model. In particular, we take into account the projection onto the physical parity sectors, required for identifying the topological degeneracy of the model. Our work opens the possibility to detect thermal metal behavior in spin liquid experiments.