Is the many-body-localized time crystal a stable phase
In plain words
Time crystals protected by disorder-induced localization were predicted to last forever in large systems. Since localization itself may fail in large systems, the time crystal may only be very long-lived.
Precise statement
For the disordered periodically driven Ising chain (near-perfect $\pi$ spin flips plus random Ising couplings, fields and generic perturbations), does the period-doubled response persist for infinite time as $L \to \infty$, or is its lifetime finite but parametrically long? Answer yes or no, with the lifetime scaling if no.
What would settle it
A determination, by numerics or proof, of the stability of Floquet many-body localization against avalanches in this model.
Status in the literature
Eigenstate order was observed on a 20-qubit processor (Mi et al., Nature 2022); infinite-time stability depends on the unresolved stability of MBL against avalanches.