Locating topological phase transitions using nonequilibrium signatures in local bulk observables

TL;DR

This paper demonstrates that local bulk observables in quantum systems can reveal topological phase transitions through non-analyticities after a quantum quench, providing a new method to locate critical points.

Contribution

It introduces a novel approach to detect topological phase transitions using non-equilibrium signatures in local observables, applicable to a wide class of initial states.

Findings

Signatures of topological critical points appear as non-analyticities in local observables after a quench.

The method accurately locates topological phase transitions in non-interacting fermion models.

Non-topological gap closings do not produce these non-analytic signatures.

Abstract

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.