Detecting the Chern number via quench dynamics in two independent chains

TL;DR

This paper presents a novel method to detect the Chern number, a topological invariant, by analyzing quench dynamics in two independent chains, linking 2D topological properties to 1D system features.

Contribution

It introduces a way to determine the Chern number through the linking number of loops derived from two independent chains, simplifying topological measurements.

Findings

Chern number equals the linking number of two loops.

Detection scheme demonstrated using the Qi-Wu-Zhang model.

Allows phase diagram measurement from 1D system analysis.

Abstract

The Chern number, as a topological invariant, characterizes the topological features of a 2D system and can be experimentally detected through Hall conductivity. In this work, we investigate the connection between the Chern number and the features of two independent chains. It is shown that there exists a class of 2D systems that can be mapped into two independent chains. We demonstrate that the Chern number is identical to the linking number of two loops, which are abstracted from each chain individually. This allows for the detection of the Chern number via quench dynamics in two independent chains. As an example, the Qi-Wu-Zhang (QWZ) model is employed to illustrate the scheme. Our finding provides a way to measure the phase diagram of a 2D system from the 1D systems.