Topologically ordered time crystals
arXiv:2105.09694 · doi:10.1038/s41467-024-54086-4
Abstract
We define topological time crystals, a dynamical phase of periodically driven quantum many-body systems capturing the coexistence of intrinsic topological order with the spontaneous breaking of discrete time-translation symmetry. We show that many-body localization can stabilize this phase against generic perturbations and establish some of its key features and signatures, including a dynamical, time-crystal form of the perimeter law for topological order. We link topological and ordinary time crystals through three complementary perspectives: higher-form symmetries, quantum error-correcting codes, and a holographic correspondence. We also propose an experimental realization of a surface-code-based topological time crystal for the Google Sycamore processor.
arXiv comment10 pages, 5 figures
References in corpus (62)
- Fault-tolerant quantum computation by anyons
- Supplementary information for "Quantum supremacy using a programmable superconducting processor"
- Anyons in an exactly solved model and beyond
- Surface codes: Towards practical large-scale quantum computation
- Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
- Topological quantum memory
- Generalized Global Symmetries
- String-net condensation: A physical mechanism for topological phases
- Symmetry protected topological orders and the group cohomology of their symmetry group
- Topological characterization of periodically-driven quantum systems
- Suppressing quantum errors by scaling a surface code logical qubit
- The foundations of statistical mechanics from entanglement: Individual states vs. averages
- Floquet Time Crystals
- Interacting electrons in disordered wires: Anderson localization and low-temperature transport
- Phenomenology of fully many-body-localized systems
- A phenomenology of certain many-body-localized systems
- Local conservation laws and the structure of the many-body localized states
- On the phase structure of driven quantum systems
- Quantum Time Crystals
- Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
- Canonical Typicality
- Lieb-Robinson bounds and the generation of correlations and topological quantum order
- Discrete time crystals: rigidity, criticality, and realizations
- Integrals of motion in the Many-Body localized phase
- Area laws in a many-body localized state and its implications for topological order
- Absence of Quantum Time Crystals
- Localization protected quantum order
- Classical Time Crystals
- Observation of Time-Crystalline Eigenstate Order on a Quantum Processor
- Generalized Symmetries in Condensed Matter
- Absolute Stability and Spatiotemporal Long-Range Order in Floquet systems
- A symmetry principle for Topological Quantum Order
- Constructing local integrals of motion in the many-body localized phase
- A classification of symmetry enriched topological phases with exactly solvable models
- Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
- Topological Defects on the Lattice I: The Ising model
- Phase Structure of 1d Interacting Floquet Systems I: Abelian SPTs
- 1D Many-body localized Floquet systems II: Symmetry-Broken phases
- Quantum quenches in the many-body localized phase
- Symmetry and Topological Order
- Quantum Quenches in Chern Insulators
- Observation of a symmetry-protected topological time crystal with superconducting qubits
- Abelian Floquet symmetry-protected topological phases in one dimension
- Radical chiral Floquet phases in a periodically driven Kitaev model and beyond
- Topological Holography: Towards a Unification of Landau and Beyond-Landau Physics
- Instability of many-body localized systems as a phase transition in a nonstandard thermodynamic limit
- Many-Body Localization: Stability and Instability
- Many-body localization beyond eigenstates in all dimensions
- Persistent Hall response in a quantum quench
- On the stability of many-body localization in
- Bulk Anyons as Edge Symmetries: Boundary Phase Diagrams of Topologically Ordered States
- Dynamically enriched topological orders in driven two-dimensional systems
- Defining Time Crystals via Representation Theory
- Topological Time Crystals
- Edge-entanglement spectrum correspondence in a nonchiral topological phase and Kramers-Wannier duality
- Long-lived topological time-crystalline order on a quantum processor
- Local Integrals of Motion for Topologically Ordered Many-Body Localized Systems
- Time-crystalline Topological Superconductors
- Nonlocal discrete time crystals in periodically driven surface codes
- Quantum Kramers-Wannier Duality And Its Topology
- (Non-)Abelian Kramers-Wannier duality and topological field theory
- Many-body-localization protection of eigenstate topological order in two dimensions