Topological characterization of chiral models through their long time dynamics

Abstract

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