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Topologically ordered time crystals
Thorsten B Wahl1, Bo Han2,3, Benjamin Béri4,5
1DAMTP, University of Cambridge, Cambridge, UK.
Nature Communications
|November 13, 2024
Summary
We introduce topologically ordered time crystals, a new phase of matter that breaks time-translation symmetry without needing spatial symmetries. This robust phase is stabilized by many-body localization and may be realized in quantum devices.
Area of Science:
- Quantum Many-Body Physics
- Condensed Matter Physics
- Quantum Information Science
Background:
- Time crystals are a novel phase of matter in periodically driven quantum systems, characterized by spontaneous breaking of discrete time-translation symmetry.
- Conventional time crystals require spatial order, often linked to additional symmetries like spin-flip symmetry.
- Topological order offers a robust form of spatial order that does not rely on symmetry.
Purpose of the Study:
- To define and explore a new class of time crystals: topologically ordered time crystals.
- To investigate the stabilization mechanisms and key features of these novel time crystals.
- To establish connections between topologically ordered and ordinary time crystals and explore their experimental realization.
Main Methods:
- Theoretical definition of topologically ordered time crystals based on intrinsic topological order.
- Analysis of stabilization by many-body localization against perturbations.
- Exploration of connections via higher-form symmetries, quantum error-correcting codes, and holographic correspondence.
Main Results:
- Definition of topologically ordered time crystals, a phase robustly ordered without symmetry.
- Demonstration that many-body localization stabilizes this phase.
- Identification of signatures, including a dynamical perimeter law for topological order.
Conclusions:
- Topologically ordered time crystals represent a new, robust phase of quantum matter.
- These time crystals can be stabilized by many-body localization and exhibit unique signatures.
- The findings provide a theoretical framework and suggest potential realization in programmable quantum devices like the Google Sycamore processor.
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