Fractionally quantized recurrence detection times in monitored quantum many-body systems

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 unexplored. Here, we address this gap by establishing universal lower and upper bounds for recurrence times in interacting many-body spin systems. 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 integer-quantized recurrence times. Our work demonstrates 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 Hilbert-space fragmentation, ergodicity breaking, measurements, and interaction effects. Finally, our findings have been implemented on an IBM quantum computer, revealing resonances and fractional quantization in agreement with theoretical predictions. This demonstrates the resilience of nonequilibrium topological fractional quantization to noise and highlights its potential use for benchmarking quantum devices and probing dark states.