Time-crystalline behavior in central spin models with Heisenberg interactions*

Time-crystalline behavior has been predicted and observed in quantum central-spin systems with Ising interactions subject to periodic driving. Here, we show how to create time-crystal-like phases in central-spin models with Heisenberg interactions, which can be realized in a single dot or defect system or star-shaped dot arrays. We show how to use time crystal physics to stabilize multi-qubit short-range correlated states in the presence of Heisenberg interactions by using either magnetic field gradients or additional pulses on the central spin.