Detection of quantum phase boundary at finite temperatures in two dimensional Kitaev model.

Quantum phase transitions occur when quantum fluctuation destroys order at zero temperature. With an increase in temperature, normally the thermal fluctuation wipes out any signs of this transition. For the two-dimensional Kitaev model, we have identified a physical quantity that shows algebraic divergence at a {\em finite} temperature, when an interaction parameter crosses the phase boundary for quantum phase transition. The quantity under consideration is the long time limit of the rate function related to a form of quantum fidelity under the quench of an interaction parameter. The robustness of the divergence makes the phase boundary detectable at any temperature. Our treatment is analytic and restricted to the vortex-free sector.