Recipe for Time Crystals

1. Needs non-adiabatic driving (residual correlations)

2. Escape featureless infinite temperature states

Recipe for Time Crystals

Generic (interacting) systems heats up to infinite temp states

Recipe 1: Use disorder to escape ergodicity

Recipe 2: Systems with tilted potential also results in localisation.

Can we use it for creating Time Crystals?

For interacting systems it is a bit more involved as for any finite size system with reflection symmetry does not remain localised. But in thermodynamic limit it is not a problem and does show time crystalline signatures.

Model

J is sampled from a constant tilt:

For, V, h, theta zero the system is diagonal in computational basis. And ZZ correaltions are trivial.

System is periodically kicked by,

At this special point, Eigenstates of H is degenerate and a state and its parity flip has the same eigenvalue.

Z anti comutes with P, so one can cook up cat states

that has the property

One has to ensure that they remain degenerate under external perturbation.

For any finite L a local perturbation will couple them

This will result in exponential splitting between the states

For uniform J the condition of DTC is

For other potentials, the system remains quasi degenerate as long as there is a region

Localisation is in these potential is previously established

Signature of DTC

Fluctuations around final plateau