Exponential onset of scalable entanglement via twist-and-turn dynamics in XY models

The efficient preparation of scalable multipartite entanglement is a central goal in the development of next-generation quantum devices. In this work, we show that the so-called ``twist-and-turn" (TaT) dynamics for interacting spin ensembles, generated by Hamiltonians with U(1)-symmetric interactions and with a transverse field, can offer an important resource to reach this goal. For models with sufficiently high connectivity, TaT dynamics exhibits two key features: 1) it features both scalable squeezing at short times, as well as quantum Fisher information with Heisenberg scaling at later times; and 2) scalable multipartite entanglement (up to Heisenberg scaling) is reached in a time growing only logarithmically with system size, associated with an exponential buildup of quantum correlations. These results can be shown exactly in the XY model with a Rabi field and infinite range interactions, and numerically in the case of spatially decaying XY interactions, such as dipolar interactions in two dimensions, provided that unstable spin-wave modes do not develop for large system sizes and/or strong fields. For dipolar interactions, the entanglement dynamics at intermediate times is completely at odds with thermalization; and it appears to saturate the maximum speed of entanglement buildup allowed by Lieb-Robinson bounds generalized to power-law interacting systems.