Floquet heating, prethermalization and time crystals

4 problems

• Is the many-body-localized time crystal a stable phase

  Contested

  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.

• Prethermal time crystal in a clean short-range two-dimensional lattice

  Open

  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.

• Heating time under quasiperiodic driving at high frequency

  Open

  Driving with two frequencies whose ratio is irrational is less regular than periodic driving, and heating is expected to be faster. The exact law relating heating time to drive frequency is not pinned down.

• Heating rate of driven bosons with unbounded local energy

  Partially resolved

  For spins driven fast, heating is known to be exponentially slow in the drive frequency. For quantum bosons, where many particles can occupy one site, no such result has been proven.