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Discrete Time Crystals: Rigidity, Criticality, and Realizations.

N Y Yao¹, A C Potter^1,2, I-D Potirniche¹

¹Department of Physics, University of California Berkeley, Berkeley, California 94720, USA.

Physical Review Letters

|February 4, 2017

Summary

We show that discrete time crystals, forbidden in equilibrium, can emerge in periodically driven systems. This study reveals their rigidity and proposes a realizable ion-based experimental blueprint.

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Area of Science:

Quantum physics
Condensed matter physics
Non-equilibrium dynamics

Background:

Spontaneous breaking of time translation symmetry is forbidden in equilibrium.
Periodically driven (Floquet) systems with discrete time-translation symmetry can exhibit time crystals.
Discrete time crystals have quantized periods arising from synchronization and many-body localization.

Purpose of the Study:

Investigate a simple model for a one-dimensional discrete time crystal.
Analyze the rigidity of emergent oscillations with varying drive parameters.
Map the phase diagram and study the dynamical phase transition to a Floquet insulator.

Main Methods:

Numerical phase diagram mapping.
Calculation of dynamical phase transition properties.
Proposal of an experimental realization using trapped ions.

Main Results:

The model exhibits rigidity in emergent oscillations.
The phase diagram reveals a transition to a Floquet insulator.
Experimental realization with trapped ions is feasible, including identification of phase boundaries.

Conclusions:

Discrete time crystals are robust phenomena in driven quantum systems.
The proposed ion-chain model offers a pathway for experimental verification.
A measurable signature for the symmetry-breaking phase transition is identified.