Random-matrix theory of measurement-induced phase transitions in nonlocal Floquet quantum circuits

Monitored quantum circuits and measurement-induced phase transitions (MIPTs) have attracted a lot attention as a result of the novel physics appearing due to the interplay of the unitary dynamics and measurements. In this work, we introduce and study a nonlocal monitored Floquet quantum circuit model that exhibits analytically treatable forced MIPT. We focus on spectral and dynamical signatures of the transition. Remarkably, we find a transition in the spectrum of the defect operator between the phase with and without a spectral gap.  In contrast to the measurement-induced transitions discussed in a number of previous works, the gap closing in the spectrum of this operator corresponds to physical observables that can be measured experimentally.