Signature of quantum phase transition manifested in quantum fidelity at zero and finite temperatures

The signature of quantum phase transition is generally wiped out at finite temperature. A few quantities that has been observed to carry this signature through a non-analytic behavior are also limited to low temperatures only. However, we have recently constructed a function from the quantum fidelity which has the potential to bear a non-analytic signature at the quantum critical point beyond low temperature regime. We demonstrate the behavior of the corresponding rate function and the robustness of the non-analyticity over a number of many-body Hamiltonians in different dimensions. We have also shown that our rate function reduces to that used in the demonstration of the dynamical quantum phase transition (DQPT) at zero temperature. It has been further observed that, unlike DQPT, the long time limit of the rate function can faithfully detect the equilibrium quantum phase transition as well.