We consider the evolution of continuously measured many-body chaotic quantum systems. Focusing on the dynamics of state purification, we analytically describe the limits of strong and weak measurement rate, where the latter case is challenging in that monitoring up to time scales exponentially long in the numbers of particles is required. We complement the analysis of the limiting regimes with the construction of an effective replica theory providing information on the stability and the symmetries of the respective phases. The analytical results are tested by comparison to exact diagonalization.

• Received 25 January 2022
• Accepted 3 June 2022

DOI:https://doi.org/10.1103/PhysRevResearch.4.L022066

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Published by the American Physical Society