2021/03/31 by Jiabin Yu, Yang Ge, Sankar Das Sarma
Mathematics · Physics and Astronomy · #Floquet theory #Geometry #Hamiltonian (control theory) #Homogeneous space #Lattice (music) #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantum and electron transport phenomena #Quantum many-body systems #Quantum mechanics #Topology (electrical circuits) #cond-mat.mes-hall #cond-mat.other #quant-ph
paper · pdf · doi:10.1103/physrevb.104.l180303
published as Phys. Rev. B 104, L180303 (2021) · Close to the published version
arxiv created 2021/11/09 · openalex publication_date 2021/11/09 · arxiv updated 2021/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Although fragile topology has been intensely studied in static crystals in terms of Wannier obstruction, it is not clear how to generalize the concept to dynamical systems. In this work we generalize the concept of fragile topology, and provide a definition of fragile topology for noninteracting Floquet crystals, which we refer to as dynamical fragile topology. In contrast to the static fragile topology defined by Wannier obstruction, dynamical fragile topology is defined for the nontrivial quantum dynamics characterized by the obstruction to static limits (OTSL). Specifically, the OTSL of a Floquet crystal is fragile if and only if it disappears after adding a symmetry-preserving static Hamiltonian in a direct-sum way preserving the relevant gaps (RGs). We further present a concrete 2+1D example for dynamical fragile topology, based on a model that is qualitatively the same as the dynamical model with anomalous chiral edge modes in Rudner et al. [Phys. Rev. X 3, 031005 (2013)]. The fragile OTSL in the 2+1D example exhibits anomalous chiral edge modes for a natural open boundary condition, and does not require any crystalline symmetries besides lattice translations. Our work paves the way to study fragile topology for general quantum dynamics.