Topology in the space-time scaling limit of quantum dynamics

TL;DR

This paper explores how topology manifests in the space-time scaling limit of quantum quench dynamics, revealing a dynamical winding number and Berry phase behavior that characterize the system's topological properties.

Contribution

It introduces a new dynamical notion of topology via a winding number based on the Berry phase response, applicable in the space-time scaling limit of quantum quenches.

Findings

Dynamical winding number encodes topology in the scaling limit.

Berry phase exhibits staircase behavior with quantized plateaus.

Topological features relate to interband DC current elements.

Abstract

We investigate the role of topology in the space-time scaling limit of quantum quench dynamics, where both time and system size tend to infinity at a constant ratio. There, while the standard topological characterization relying on local unitary transformations becomes ill defined, we show how a different dynamical notion of topology naturally arises through a dynamical winding number encoding the linear response of the Berry phase to a magnetic flux. Specifically, we find that the presence of a locally invisible constant magnetic flux is revealed by a dynamical staircase behavior of the Berry phase, whose topologically quantized plateaus characterize the space-time scaling limit of a quenched Rice-Mele model. These jumps in the Berry phase are also shown to be related to the interband elements of the DC current operator. We outline possible experimental platforms for observing the predicted phenomena in finite systems.