Universal fluctuations of Floquet topological invariants at low frequencies

Abstract

We study the low-frequency dynamics of periodically driven one-dimensional systems hosting Floquet topological phases. We show, both analytically and numerically, in the low-frequency limit $\Omega \to 0$, the topological invariants of a chirally-symmetric driven system exhibit universal fluctuations. While the topological invariants in this limit nearly vanish on average over a small range of frequencies, we find that they follow a universal Gaussian distribution with a width that scales as $1/\sqrt{\Omega }$. We explain this scaling based on a diffusive structure of the winding numbers of the Floquet-Bloch evolution operator at low frequency. We also find that the maximum quasienergy gap remains finite and scales as ${\Omega }^2$. Thus, we argue that the adiabatic limit of a Floquet topological insulator is highly structured, with universal fluctuations persisting down to very low frequencies.

In this version we present additional numerical results for the topological invariants of the SSH, Kitaev, and SSH-Kitaev models in the low-frequency regime. The draft has 5 pages, and 11 figures

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• Non-Hermitian Floquet topological phases: Exceptional points, coalescent edge modes, and the skin effect
• Generating a second-order topological insulator with multiple corner states by periodic driving
• Floquet Perturbation Theory: Formalism and Application to Low-Frequency Limit
• Non-Hermitian Floquet topological phases in the double-kicked rotor
• Effective Floquet Hamiltonian in the low-frequency regime
• Floquet topological phase transitions in a periodically quenched dimer
• Floquet engineering to exotic topological phases in systems of cold atoms
• How to Directly Measure Floquet Topological Invariants in Optical Lattices
• Floquet engineering of twisted double bilayer graphene
• Linear Response Theory and Optical Conductivity of Floquet Topological Insulators
• Gauge-induced Floquet topological states in photonic waveguides
• Driven quantum many-body systems and out-of-equilibrium topology
• Generalized bulk-boundary correspondence in periodically driven non-Hermitian systems
• Floquet topological phases with fourfold-degenerate edge modes in a driven spin-1/2 Creutz ladder
• Chiral 1D Floquet topological insulators beyond rotating wave approximation
• Critical phase boundaries of static and periodically kicked long-range Kitaev chain
• Chiral limits and effect of light on the Hofstadter butterfly in twisted bilayer graphene
• Floquet band engineering with Bloch oscillations
• Topological edge states at Floquet quantum criticality
• Floquet Engineering with Particle Swarm Optimization: Maximizing Topological Invariants
• Floquet topological insulators: from band structure engineering to novel non-equilibrium quantum phenomena
• Quantum noise detects Floquet topological phases
• Quantum Hall edge states under periodic driving: a Floquet induced chirality switch
• Disconnected entanglement entropy as a marker of edge modes in a periodically driven Kitaev chain
• Topological characterization of a non-Hermitian ladder via Floquet non-Bloch theory
• Light driven magnetic transitions in transition metal dichalcogenide heterobilayers
• Effects of topological and non-topological edge states on information propagation and scrambling in a Floquet spin chain
• Floquet non-Abelian topological charges and edge states
• The Future of the Correlated Electron Problem
• Direct driving of electronic and phononic degrees of freedom in a honeycomb bilayer with infrared light
• The quantum phase transitions of dimer chain driven by an imaginary ac field
• Floquet Möbius topological insulators
• Low-frequency and Moiré Floquet engineering: a review
• Floquet engineering and non-equilibrium topological maps in twisted trilayer graphene
• Topology and edge modes surviving criticality in non-Hermitian Floquet systems