Detecting Bulk Topology of Quadrupolar Phase from Quench Dynamics

TL;DR

This paper proposes a method to detect the bulk topological properties of a quantum quadrupole insulator using quench dynamics, introducing a new measurable quantity that distinguishes topological phases.

Contribution

It introduces a novel quadrupole moment weighted by chiral eigenvalues as a topological indicator, applicable to both noninteracting and interacting systems, and demonstrates robustness against disorder.

Findings

The proposed quantity differentiates trivial and topological phases.

Numerical tracking confirms its effectiveness in various cases.

Robustness against disorder is established.

Abstract

Direct measurement of a bulk topological observable in topological phase of matter has been a long-standing issue. Recently, detection of bulk topology through quench dynamics has attracted growing interests. Here, we propose that topological characters of a quantum quadrupole insulator can be read out by quench dynamics. Specifically, we introduce a quantity, a quadrupole moment weighted by the eigenvalues of the chiral operator, which takes zero for the trivial phase and finite for the quadrupolar topological phase. By utilizing an efficient numerical method to track the unitary time evolution, we elucidate that the quantity we propose indeed serves as an indicator of topological character for both noninteracting and interacting cases. The robustness against disorders is also demonstrated.