Dynamics of 2D topological quadrupole insulator and Chern insulator induced by real-space topological changes

TL;DR

This paper investigates the real-space topological transformations in 2D topological quadrupole and Chern insulators, revealing how their edge and corner states dynamically respond, with implications for quantum memory and topology inference.

Contribution

It provides a detailed analysis of the dynamical behavior of topological edge and corner states during real-space topology changes, highlighting the persistence of density ripples and steady-state behaviors.

Findings

Corner states exhibit steady-state occupation after topology change.

Density ripples persist and differ depending on the final geometry.

Steady-state values depend on the transformation rate, indicating quantum memory effects.

Abstract

The dynamics of two-dimensional (2D) topological quadrupole insulator (TQI) and Chern insulator (CI) after the real-space configuration is transformed from a cylinder or Mobius strip to open boundary condition (OBC) and vice versa is analyzed. Similar dynamics of both models are observed, but the quadrupole corner states of the TQI makes the signatures more prominent. After the systems transform from a cylinder or Mobius strip to OBC, the occupation of the corner state of the TQI and the edge state of the CI exhibits steady-state behavior. The steady-state values depend on the ramping rate of the configuration transformation, manifesting a type of quantum memory effect. On the other hand, oscillatory density ripples from the merging of edge states persist after the systems transform from OBC to a cylinder or Mobius strip. If the final configuration is a cylinder, the density ripples are along the edges of the cylinder. In contrast, the density ripples can traverse the bulk after the systems transform from OBC to a Mobius strip. The transformation of real-space topology thus can be inferred from the dynamical signatures of the topological edge states.