Characterizing Floquet topological phases by quench dynamics: A multiple-subsystem approach

TL;DR

This paper presents a flexible dynamical scheme to classify Floquet topological phases by analyzing quench dynamics in momentum subspaces, applicable to various dimensions and experimental imperfections.

Contribution

It introduces a novel approach that disassembles Floquet systems into static subsystems, simplifying the detection of topological invariants through quench dynamics along arbitrary spin axes.

Findings

Scheme successfully applied to 2D and 3D models

Method robust against initial state polarization imperfections

Enhances experimental feasibility for topological phase detection

Abstract

We investigate the dynamical characterization theory for periodically driven systems in which Floquet topology can be fully detected by emergent topological patterns of quench dynamics in momentum subspaces called band-inversion surfaces. We improve the results of a recent work [Zhang et al., Phys. Rev. Lett. 125, 183001 (2020)] and propose a more flexible scheme to characterize a generic class of $d$-dimensional Floquet topological phases classified by $\mathbb{Z}$-valued invariants by applying a quench along an arbitrary spin-polarization axis. Our basic idea is that by disassembling the Floquet system into multiple static subsystems that are periodic in quasienergy, a full characterization of Floquet topological phases reduces to identifying a series of bulk topological invariants for time-independent Hamiltonians, which greatly enhances the convenience and flexibility of the measurement. We illustrate the scheme by numerically analyzing two experimentally realizable models in two and three dimensions, respectively, and adopting two different but equivalent viewpoints to examine the dynamical characterization. Finally, considering the imperfection of experiment, we demonstrate that the present scheme can also be applied to a general situation where the initial state is not completely polarized. This study provides an immediately implementable approach for dynamically classifying Floquet topological phases in ultracold atoms or other quantum simulators.