Topologically ordered time crystals

Thorsten B. Wahl, Bo Han and Benjamin Béri ()
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Thorsten B. Wahl: University of Cambridge
Bo Han: Weizmann Institute of Science
Benjamin Béri: University of Cambridge

Nature Communications, 2024, vol. 15, issue 1, 1-8

Abstract: 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.

Date: 2024
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DOI: 10.1038/s41467-024-54086-4

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