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.
10 pages, 5 figures
References in corpus (21)
- Supplementary information for "Quantum supremacy using a programmable superconducting processor"
- Surface codes: Towards practical large-scale quantum computation
- Generalized Global Symmetries
- Topological characterization of periodically-driven quantum systems
- Suppressing quantum errors by scaling a surface code logical qubit
- Phenomenology of fully many-body-localized systems
- Lieb-Robinson bounds and the generation of correlations and topological quantum order
- Integrals of motion in the Many-Body localized phase
- Absence of Quantum Time Crystals
- Observation of Time-Crystalline Eigenstate Order on a Quantum Processor
- Generalized Symmetries in Condensed Matter
- Constructing local integrals of motion in the many-body localized phase
- A classification of symmetry enriched topological phases with exactly solvable models
- Quantum quenches in the many-body localized phase
- Observation of a symmetry-protected topological time crystal with superconducting qubits
- 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
- Edge-entanglement spectrum correspondence in a nonchiral topological phase and Kramers-Wannier duality
- Long-lived topological time-crystalline order on a quantum processor
- Nonlocal discrete time crystals in periodically driven surface codes
- Many-body-localization protection of eigenstate topological order in two dimensions