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Quantum phase transitions occur when quantum fluctuation destroys order atzero temperature. With an increase in temperature, normally the thermalfluctuation wipes out any signs of this transition. Here we identify a physicalquantity that shows non-analytic behaviour at finite temperatures, when aninteraction parameter is quenched across the line of quantum phase transition.This quantity under consideration is the long time limit of a form of quantumfidelity. Our treatment is analytic for XY chain and 2D Kitaev model and isnumerical for a 3D Hamiltonian applicable to Weyl semimetals.

Detection of quantum phase boundary at finite temperatures in integrable spin models