Floquet Topological Order in Interacting Systems of Bosons and Fermions

Abstract

Periodically driven noninteracting systems may exhibit anomalous chiral edge modes, despite hosting bands with trivial topology. We find that these drives have surprising many-body analogs, corresponding to class A, which exhibit anomalous charge and information transport at the boundary. Drives of this form are applicable to generic systems of bosons, fermions, and spins, and may be characterized by the anomalous unitary operator that acts at the edge of an open system. We find that these operators are robust to all local perturbations and may be classified by a pair of coprime integers. This defines a notion of dynamical topological order that may be applied to general time-dependent systems, including many-body localized phases or time crystals.

5 pages plus references and supplemental material; v2 is published version, with title change and new introduction

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• Periodically, Quasi-periodically, and Randomly Driven Conformal Field Theories (II): Furstenberg's Theorem and Exceptions to Heating Phases
• Quantum information geometry of driven CFTs
• Topology and localization of a periodically driven Kitaev model
• Topological lower bound on quantum chaos by entanglement growth
• Topological phase transitions at finite temperature
• Cross-dimensional universality classes in static and periodically driven Kitaev models
• The Real-Time Correlation Function of Floquet Conformal Fields
• Fractionalized Prethermalization in a Driven Quantum Spin Liquid
• Dynamics and Control of Edge States in Laser-driven Graphene Nanoribbons
• Coarse-grained Entanglement and Operator Growth in Anomalous Dynamics
• The Streda Formula for Floquet Systems: Topological Invariants and Quantized Anomalies from Cesaro Summation
• Many-body localization crossover is sharper in quasiperiodic spin chains
• Light driven magnetic transitions in transition metal dichalcogenide heterobilayers
• Information Flow in Non-Unitary Quantum Cellular Automata
• Floquet Amorphous Topological Orders in a One-dimensional Rydberg Glass
• Moment method and continued fraction expansion in Floquet Operator Krylov Space
• Topological Phases of Many-Body Localized Systems: Beyond Eigenstate Order
• Proposal for realizing anomalous Floquet insulators via Chern band annihilation
• Floquet-Engineering Weyl Points and Linked Fermi Arcs from Straight Nodal Lines
• Low-frequency and Moiré Floquet engineering: a review
• Engineering micromotion in Floquet prethermalization via space-time symmetries