  Recurrence time quantifies the duration required for a physical system to
return to its initial state, playing a pivotal role in understanding the
predictability of complex systems. In quantum systems with subspace
measurements, recurrence times are governed by Anandan-Aharonov phases,
yielding fractionally quantized recurrence times. However, the fractional
quantization phenomenon in interacting quantum systems remains poorly explored.
Here, we address this gap by establishing universal lower and upper bounds for
recurrence times in interacting spins. Notably, we investigate scenarios where
these bounds are approached, shedding light on the speed of quantum processes
under monitoring. In specific cases, our findings reveal that the complex
many-body system can be effectively mapped onto a dynamical system with a
single quasi-particle, leading to the discovery of integer quantized recurrence
times. Our research yields a valuable link between recurrence times and the
number of dark states in the system, thus providing a deeper understanding of
the intricate interplay between quantum recurrence, measurements, and
interaction effects.
