Topological characterization of chiral models through their long time dynamics

TL;DR

This paper introduces a method to determine the topological properties of one-dimensional chiral models by analyzing their long-term dynamics through the mean chiral displacement, applicable to various non-interacting systems.

Contribution

It provides a spectral projector-based approach to detect topological invariants in static and driven chiral systems using long-time bulk measurements.

Findings

Rapid convergence of the detection method

Applicable to all non-interacting chiral systems

Measures arbitrary winding numbers and topological boundaries

Abstract

We study chiral models in one spatial dimension, both static and periodically driven. We demonstrate that their topological properties may be read out through the long time limit of a bulk observable, the mean chiral displacement. The derivation of this result is done in terms of spectral projectors, allowing for a detailed understanding of the physics. We show that the proposed detection converges rapidly and it can be implemented in a wide class of chiral systems. Furthermore, it can measure arbitrary winding numbers and topological boundaries, it applies to all non-interacting systems, independently of their quantum statistics, and it requires no additional elements, such as external fields, nor filled bands.