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Topologically ordered time crystals

Author

Listed:
  • Thorsten B. Wahl

    (University of Cambridge)

  • Bo Han

    (Weizmann Institute of Science
    University of Cambridge)

  • Benjamin Béri

    (University of Cambridge
    University of Cambridge)

Abstract

Time crystals are a dynamical phase of periodically driven quantum many-body systems where discrete time-translation symmetry is broken spontaneously. Time-crystallinity however subtly requires also spatial order, ordinarily related to further symmetries, such as spin-flip symmetry when the spatial order is ferromagnetic. Here we define topologically ordered time crystals, a time-crystalline phase borne out of intrinsic topological order—a particularly robust form of spatial order that requires no 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 topologically ordered and ordinary time crystals through three complementary perspectives: higher-form symmetries, quantum error-correcting codes, and a holographic correspondence. Topologically ordered time crystals may be realized in programmable quantum devices, as we illustrate for the Google Sycamore processor.

Suggested Citation

  • Thorsten B. Wahl & Bo Han & Benjamin Béri, 2024. "Topologically ordered time crystals," Nature Communications, Nature, vol. 15(1), pages 1-8, December.
    • Handle: RePEc:nat:natcom:v:15:y:2024:i:1:d:10.1038_s41467-024-54086-4
    DOI: 10.1038/s41467-024-54086-4
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