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Topologically ordered time crystals.

Thorsten B Wahl¹, Bo Han^2,3, Benjamin Béri^4,5

¹DAMTP, University of Cambridge, Cambridge, UK.

Nature Communications

|November 13, 2024

Summary

This summary is machine-generated.

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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:

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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.