Topological time crystals

@article{Giergiel2018TopologicalTC,
  title={Topological time crystals},
  author={Krzysztof Giergiel and Alexandre Dauphin and Maciej Lewenstein and Jakub J. Zakrzewski and Krzysztof Sacha},
  journal={New Journal of Physics},
  year={2018},
  volume={21}
}
By analogy with the formation of space crystals, crystalline structures can also appear in the time domain. While in the case of space crystals we often ask about periodic arrangements of atoms in space at a moment of a detection, in time crystals the role of space and time is exchanged. That is, we fix a space point and ask if the probability density for detection of a system at this point behaves periodically in time. Here, we show that in periodically driven systems it is possible to realize… 

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References

SHOWING 1-10 OF 113 REFERENCES

Three-Dimensional Localized-Delocalized Anderson Transition in the Time Domain.

It is shown that a three- dimensional system exposed to a properly disordered pseudoperiodic driving may display a localized-delocalized Anderson transition in the time domain, in strong analogy with the usual three-dimensional Anderson Transition in disordered systems.

Clean Floquet Time Crystals: Models and Realizations in Cold Atoms.

It is pointed out that time crystals can generally exist in systems without disorder, and a series of clean quasi-one-dimensional models under Floquet driving are proposed to demonstrate this unexpected result in principle.

Observation of a discrete time crystal

The experimental observation of a discrete time crystal, in an interacting spin chain of trapped atomic ions, is presented, which opens the door to the study of systems with long-range spatio-temporal correlations and novel phases of matter that emerge under intrinsically non-equilibrium conditions.

Time crystals: Analysis of experimental conditions

Time crystals are quantum many-body systems which are able to self-organize their motion in a periodic way in time. Discrete time crystals have been experimentally demonstrated in spin systems.

Synthesizing lattice structures in phase space

In one dimensional systems, it is possible to create periodic structures in phase space through driving, which is called phase space crystals (Guo et al 2013 Phys. Rev. Lett. 111 205303). This is

Time Crystal Platform: From Quasicrystal Structures in Time to Systems with Exotic Interactions.

Here it is shown that condensed matter problems ranging from single particles in potentials of quasicrystal structure to many-body systems with exotic long-range interactions can be realized in the time domain with an appropriate periodic driving.

Discrete Time Crystals: Rigidity, Criticality, and Realizations.

A simple model for a one-dimensional discrete time crystal which explicitly reveals the rigidity of the emergent oscillations as the drive is varied is considered and a blueprint based upon a one dimensional chain of trapped ions is proposed.

Synthesizing lattice structures in phase space

In one dimensional systems, it is possible to create periodic structures in phase space through driving, which is called phase space crystals (Guo et al 2013 Phys. Rev. Lett. 111 205303). This is

Absence of Quantum Time Crystals.

A no-go theorem is proved that rules out the possibility of time crystals defined as such, in the ground state or in the canonical ensemble of a general Hamiltonian, which consists of not-too-long-range interactions.

Space-Time Crystal and Space-Time Group.

A new group structure dubbed a "space-time" group is constructed to describe the discrete symmetries of a space-time crystal characterized by the general intertwined space- time periodicities in D+1 dimensions, which include both the static crystal and the Floquet crystal as special cases.
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