Locating topological phase transitions using nonequilibrium signatures in local bulk observables

Topological quantum phases cannot be characterized by local order parameters in the bulk. In this work, however, we show that nonanalytic signatures of a topological quantum critical point do remain in local observables in the bulk, and manifest themselves as nonanalyticities in their expectation values taken over a family of nonequilibrium states generated using a quantum quench protocol. The signature can be used for precisely locating the critical points in parameter space. A large class of initial states can be chosen for the quench, including finite temperature states. We demonstrate these results in tractable models of noninteracting fermions exhibiting topological phase transitions in one and two spatial dimensions. We also show that the nonanalyticities can be absent if the gap closing is nontopological, i.e., when it corresponds to no phase transition.