Floquet topological phases with symmetry in all dimensions

Abstract

Dynamical systems may host a number of remarkable symmetry-protected phases that are qualitatively different from their static analogs. In this work, we consider the phase space of symmetry-respecting unitary evolutions in detail and identify several distinct classes of evolution that host novel dynamical order. Using ideas from group cohomology, we construct a set of interacting Floquet drives that generate dynamical symmetry-protected topological order for each nontrivial cohomology class in every dimension, illustrating our construction with explicit two-dimensional examples. We also identify a set of symmetry-protected Floquet drives that lie outside of the group cohomology construction, and a further class of symmetry-respecting topological drives which host chiral edge modes. We use these special drives to define a notion of phase (stable to a class of local perturbations in the bulk) and the concepts of relative and absolute topological order, which can be applied to many different classes of unitary evolutions. These include fully many-body localized unitary evolutions and time crystals.

18 pages, 10 figures. v2: updated references, two new figures, minor changes throughout

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Cited by in corpus (68)

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• Topological Floquet-Thouless energy pump
• Integrable many-body quantum Floquet-Thouless pumps
• Floquet Quantum Criticality
• Quantum Cellular Automata, Tensor Networks, and Area Laws
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• Floquet Majorana zero and $\pi$ modes in planar Josephson junctions
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• Localization counteracts decoherence in noisy Floquet topological chains
• On adiabatic cycles of quantum spin systems
• Entanglement properties of the time periodic Kitaev Chain
• Strong-Disorder Renormalization Group for Periodically Driven Systems
• Many-body dynamics and gap opening in interacting periodically driven systems
• Unified Light-Matter Floquet Theory and its Application to Quantum Communication
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• Boundary states of Three Dimensional Topological Order and the Deconfined Quantum Critical Point
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• Prethermalization and entanglement dynamics in interacting topological pumps
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• Interacting topological frequency converter
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• Topological Quantum Walk with Discrete Time-Glide Symmetry
• Quantized Floquet topology with temporal noise
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• Interacting Floquet topological phases in three dimensions
• Electronic Floquet Liquid Crystals
• Gauging anomalous unitary operators
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• Tunable interface states between Floquet-Weyl semimetals
• Gappability Index for Quantum Many-Body Systems
• Non-local finite-depth circuits for constructing SPT states and quantum cellular automata
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• Quantum quench in a driven Ising chain
• Coupled Layer Construction for Synthetic Hall Effects in Driven Systems
• Moment method and continued fraction expansion in Floquet Operator Krylov Space
• Dynamical Chiral Symmetry and Symmetry-Class Conversion in Floquet Topological Insulators
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• Universality in Non-Equilibrium Quantum Systems
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• Floquet dynamics of disordered bands with isolated critical energies
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• Phase Transition of Topological Index driven by Dephasing