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Recurrence time quantifies the duration required for a physical system toreturn to its initial state, playing a pivotal role in understanding thepredictability of complex systems. In quantum systems with subspacemeasurements, recurrence times are governed by Anandan-Aharonov phases,yielding fractionally quantized recurrence times. However, the fractionalquantization phenomenon in interacting quantum systems remains poorly explored.Here, we address this gap by establishing universal lower and upper bounds forrecurrence times in interacting spins. Notably, we investigate scenarios wherethese bounds are approached, shedding light on the speed of quantum processesunder monitoring. In specific cases, our findings reveal that the complexmany-body system can be effectively mapped onto a dynamical system with asingle quasi-particle, leading to the discovery of integer quantized recurrencetimes. Our research yields a valuable link between recurrence times and thenumber of dark states in the system, thus providing a deeper understanding ofthe intricate interplay between quantum recurrence, measurements, andinteraction effects.

Properties of Fractionally Quantized Recurrence Times for Interacting Spin Models