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 signatures of a topological quantum critical point do remain in local observables in the bulk, and manifest themselves as non-analyticities in their expectation values taken over a family of non-equilibrium 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), the sufficient condition being existence of a finite occupation-gradient with respect to energy for the single-particle critical mode. We demonstrate these results in tractable models of non-interacting fermions exhibiting topological phase transitions in one and two spatial dimensions. We also show that the non-analyticities can be absent if the gap-closing is non-topological, i.e., when it corresponds to no phase transition.