Dynamically enriched topological orders in driven two-dimensional systems

Abstract

Time-periodic driving of a quantum system can enable new dynamical topological phases of matter that could not exist in thermal equilibrium. We investigate two related classes of dynamical topological phenomena in 2D systems: Floquet symmetry protected topological phases (FSPTs), and Floquet enriched topological orders (FETs). By constructing solvable lattice models for a complete set of 2D bosonic FSPT phases, we show that bosonic FSPTs can be understood as topological pumps which deposit loops of 1D SPT chains onto the boundary during each driving cycle, which protects a non-trivial edge state by dynamically tuning the edge to a self-dual point poised between the 1D SPT and trivial phases of the edge. By coupling these FSPT models to dynamical gauge fields, we construct solvable models of FET orders in which anyon excitations are dynamically transmuted into topologically distinct anyon types during each driving period. These bosonic FSPT and gauged FSPT models are classified by group cohomology methods. In addition, we also construct examples of "beyond cohomology" FET orders, which can be viewed as topological pumps of 1D topological chains formed of emergent anyonic quasi-particles.

14 pages, 2 figures, v2 - substantially expanded discussion of properties of Floquet enriched topological orders

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Cited by in corpus (51)

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• Radical chiral Floquet phases in a periodically driven Kitaev model and beyond
• Long-lived interacting phases of matter protected by multiple time-translation symmetries in quasiperiodically-driven systems
• Anomalous Floquet Insulators
• Topological Floquet-Thouless energy pump
• Interacting invariants for Floquet phases of fermions in two dimensions
• Space-time crystal and space-time group
• Bosonic topological phases of matter: bulk-boundary correspondence, SPT invariants and gauging
• Quantum Cellular Automata, Tensor Networks, and Area Laws
• Codimension-2 defects and higher symmetries in (3+1)D topological phases
• Pivot Hamiltonians as generators of symmetry and entanglement
• Minimalist approach to the classification of symmetry protected topological phases
• Absence of Thermalization in Finite Isolated Interacting Floquet Systems
• Three-dimensional quantum cellular automata from chiral semion surface topological order and beyond
• Cavity magnon-polaritons in cuprate parent compounds
• Classification of Matrix-Product Unitaries with Symmetries
• Disorder induced transitions in resonantly driven Floquet Topological Insulators
• Searching for Fracton Orders via Symmetry Defect Condensation
• Topological edge modes without symmetry in quasiperiodically driven spin chains
• Classification of interacting Floquet phases with $U(1)$ symmetry in two dimensions
• Topological lower bound on quantum chaos by entanglement growth
• Fermionic quantum cellular automata and generalized matrix product unitaries
• Critical Theory for the Breakdown of Photon Blockade
• On adiabatic cycles of quantum spin systems
• Long-lived topological time-crystalline order on a quantum processor
• Optically induced topological states on the surface of mercury telluride
• Effective response theory for Floquet topological systems
• An infinite family of 3d Floquet topological paramagnets
• Symmetric Finite-Time Preparation of Cluster States via Quantum Pumps
• Quantized Floquet topology with temporal noise
• Coarse-grained Entanglement and Operator Growth in Anomalous Dynamics
• Interacting Floquet topological phases in three dimensions
• Stable measurement-induced Floquet enriched topological order
• A Universal Model of Floquet Operator Krylov Space
• Superuniversality from disorder at two-dimensional topological phase transitions
• Non-local finite-depth circuits for constructing SPT states and quantum cellular automata
• Topologically ordered time crystals
• Information Flow in Non-Unitary Quantum Cellular Automata
• Quantum cellular automata and categorical dualities of spin chains
• Moment method and continued fraction expansion in Floquet Operator Krylov Space
• Charge pumps, pivot Hamiltonians and symmetry-protected topological phases
• Lieb-Robinson Bounds on Entanglement Gaps from Symmetry-Protected Topology
• Spacetime symmetry-enriched SymTFT: from LSM anomalies to modulated symmetries and beyond
• Anomalies of global symmetries on the lattice
• Competing automorphisms and disordered Floquet codes
• Orbital magnetization of Floquet topological systems
• Floquet topological systems with flat bands: Edge modes, Berry curvature, and Orbital magnetization
• Universal fault tolerant quantum computation in 2D without getting tied in knots
• Phases of Floquet code under local decoherence