Anomalous waiting-time distributions in postselection-free quantum many-body dynamics under continuous monitoring

We investigate waiting-time distributions (WTDs) of quantum jumps in continuously monitored quantum many-body systems, whose unconditional dynamics lead to the trivial infinite-temperature state. We demonstrate that the WTD of a half-chain subsystem exhibits an anomalous tail, markedly deviating from the Poissonian distribution in stark contrast to that of the whole system. By analyzing the spectral properties of the superoperator mathscr L₀, which is defined by removing the jump terms associated with the half-chain subsystem from the full Liouvillian, we find that the long-time behavior with the anomalous tail of the half-chain WTD is governed by the eigenvalue λ₀ (<0) with the largest real part. We further reveal a qualitative change in the system-size dependence of λ₀ as a function of the measurement strength: for sufficiently weak measurement, λ₀ decreases proportionally to the system size, while for strong measurement, λ₀ scales independently of the system size, signaling the persistence of the anomalous half-chain WTD in the thermodynamic limit. The WTD is extracted solely from the spacetime record of quantum jumps \{t_i,x_i\} and can be experimentally accessed without postselection. Our work establishes a spectral framework for understanding nontrivial WTDs in subsystems of monitored quantum dynamics and provides a novel diagnostics to assess many-body effects on WTDs.