Prethermal time crystal in a clean short-range two-dimensional lattice
In plain words
Without disorder, a fast drive can still keep a time crystal alive for a time that grows exponentially with drive frequency, but theory says this needs long-range interactions or at least two dimensions. Existing observations used long-range or dipolar interactions.
Precise statement
For a periodically driven spin lattice with short-range couplings of strength $J$, drive frequency $\omega >> J/\hbar$ and near-$\pi$ spin flips, prethermal theory (Else, Bauer, Nayak, PRX 7, 011026, 2017) predicts period-doubled response lasting t* ~ exp(c hbar omega/J); at finite energy density this needs spontaneous breaking of an emergent Ising symmetry of the prethermal Hamiltonian, hence $d \ge 2$ for short-range couplings. Does a $d = 2$ short-range system show t* growing exponentially with $\omega$, and does the response vanish above the critical energy density of the prethermal Ising transition? Answer yes or no, with t*(omega).
What would settle it
Measurement in a 2D Rydberg or superconducting-qubit array, or large-scale numerics, of the period-doubled lifetime versus $\omega$ and initial energy density.
Status in the literature
Observed with long-range interactions in a trapped-ion chain (Kyprianidis et al., Science 2021) and with dipolar couplings in 3D nuclear-spin ensembles (Beatrez et al., Nature Physics 2023; Stasiuk et al., PRX 2023); a 2D short-range test is not known (low confidence).